Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
63326 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.
This group has 63326 conjugacy classes of subgroups — too many to draw. Only its 34795 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. C24×Dic26 | C2 | semidirect |
| 2. C23×Q8×D13 | C2 | direct (N × H) |
| 4. C24×Q8×C13 | C2 | semidirect |
| 6. C23×Q8×C13 | C22 | semidirect |
| 9. C22×Q8×D13 | C22 | direct (N × H) |
| 11. C23×Dic26 | C22 | semidirect |
| 13. C24×D13 | Q8 | direct (N × H) |
| 15. C22×Q8×C13 | C23 | semidirect |
| 18. C2×Q8×D13 | C23 | direct (N × H) |
| 20. C22×Dic26 | C23 | semidirect |
| 22. C24×C13 | C2×Q8 | semidirect |
| 24. C23×D13 | C2×Q8 | direct (N × H) |
| 26. C2×Q8×C13 | C24 | semidirect |
| 29. Q8×D13 | C24 | direct (N × H) |
| 31. C2×Dic26 | C24 | semidirect |
| 34. C24×Q8 | D13 | direct (N × H) |
| 36. C23×C13 | C22×Q8 | semidirect |
| 38. C22×D13 | C22×Q8 | direct (N × H) |
| 40. Q8×C13 | C25 | semidirect |
| 44. Dic26 | C25 | semidirect |
| 48. C23×Q8 | C2×D13 | direct (N × H) |
| 52. C22×C13 | C23×Q8 | semidirect |
| 54. C2×D13 | C23×Q8 | direct (N × H) |
| 63. C22×Q8 | C22×D13 | direct (N × H) |
| 67. C2×C13 | C24×Q8 | semidirect |
| 69. D13 | C24×Q8 | direct (N × H) |
| 72. C24 | Q8×D13 | direct (N × H) |
| 76. C2×Q8 | C23×D13 | direct (N × H) |
| 80. C13 | C25×Q8 | semidirect |
| 83. C23 | C2×Q8×D13 | direct (N × H) |
| 86. Q8 | C24×D13 | direct (N × H) |
| 92. C22 | C22×Q8×D13 | direct (N × H) |
| 97. C2 | C23×Q8×D13 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic26 | 2 |
| C23×Q8×D13 | 2 |
| C24×C4×D13 | 2 |
| C24×Q8×C13 | 2 |
| C25×Q8 | 13 |