Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 6044 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has at least 6044 conjugacy classes of subgroups — too many to draw. Only its 295 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11715572 | C2 | semidirect |
| 2. C22×D4×C22⋊A4 | C2 | semidirect |
| 3. C22×#87524 | C2 | semidirect |
| 4. C2×#11715569 | C2 | semidirect |
| 5. #72216669 | C2 | direct (N × H) |
| 6. C24×#1020 | C2 | semidirect |
| 8. C23×#1020 | C22 | semidirect |
| 9. C2×#87524 | C22 | semidirect |
| 10. C22×#5936 | C22 | semidirect |
| 11. #11715572 | C22 | semidirect |
| 12. #11715569 | C22 | semidirect |
| 14. C24×C22⋊A4 | C22 | semidirect |
| 15. C2×D4×C22⋊A4 | C22 | semidirect |
| 16. C22×C4×C22⋊A4 | C22 | semidirect |
| 17. C26×D4 | D3 | semidirect |
| 18. C23×C22⋊A4 | D4 | semidirect |
| 21. C23×C22⋊A4 | C23 | semidirect |
| 22. C22×#1020 | D4 | semidirect |
| 24. C2×C4×C22⋊A4 | C23 | semidirect |
| 25. C2×#5936 | C23 | semidirect |
| 27. C28 | C2×D3 | semidirect |
| 28. C25×D4 | C2×D3 | semidirect |
| 29. C26×C4 | C2×D3 | semidirect |
| 32. C22×C22⋊A4 | C2×D4 | semidirect |
| 34. C2×#1020 | C2×D4 | semidirect |
| 35. C27 | #67 | semidirect |
| 38. C27 | C22×D3 | semidirect |
| 39. C24×D4 | S4 | semidirect |
| 40. C25×C4 | C22×D3 | semidirect |
| 41. C2×C22⋊A4 | #120 | semidirect |
| 46. C26 | C2×#67 | semidirect |
| 48. C26 | C2×S4 | semidirect |
| 50. C23×D4 | C2×S4 | semidirect |
| 51. C24×C4 | C2×S4 | semidirect |
| 52. C22⋊A4 | C2×#120 | semidirect |
| 53. C25 | #937 | semidirect |
| 54. C25 | GL(2,ℤ/4) | semidirect |
| 59. C25 | C22×S4 | semidirect |
| 60. C22×D4 | #1020 | semidirect |
| 61. C23×C4 | C22×S4 | semidirect |
| 62. C24 | C2×#937 | semidirect |
| 65. C24 | C2×GL(2,ℤ/4) | semidirect |
| 68. C24 | C2×#1020 | semidirect |
| 69. C2×D4 | C2×#1020 | semidirect |
| 70. C22×C4 | C2×#1020 | semidirect |
| 71. C23 | #85493 | semidirect |
| 74. C23 | #87524 | semidirect |
| 77. C23 | C22×#1020 | semidirect |
| 78. C2×C4 | C22×#1020 | semidirect |
| 79. C22 | C2×#85493 | semidirect |
| 82. C22 | C2×#87524 | semidirect |
| 85. C2 | #72216669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11715572 | 2 |
| C22×D4×C22⋊A4 | 2 |
| C22×#87524 | 2 |
| C2×#612424 | 3 |
| C2×#11715569 | 2 |
| #72216669 | 2 |
| C24×#1020 | 2 |
| C2×#85493 | 4 |