Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20261802 | C2 | semidirect |
| 2. #20261776 | C2 | semidirect |
| 3. D8×#87604 | C2 | semidirect |
| 4. #20261745 | C2 | semidirect |
| 5. #20261727 | C2 | semidirect |
| 6. #20261698 | C2 | semidirect |
| 10. D4×#87604 | C22 | semidirect |
| 14. #15690879 | C22 | semidirect |
| 15. #15690878 | C22 | semidirect |
| 16. #15690872 | C22 | semidirect |
| 17. #15690864 | C22 | semidirect |
| 18. C8×#87604 | C22 | semidirect |
| 20. C2×D776 | C4 | semidirect |
| 21. C2×#13095496 | C4 | semidirect |
| 22. D8×D97 | C4 | semidirect |
| 23. D8×D97 | C4 | semidirect |
| 27. C2×D8×C97 | C4 | semidirect |
| 40. C2×D388 | C2×C4 | semidirect |
| 44. D4×D97 | C2×C4 | semidirect |
| 47. D776 | C2×C4 | semidirect |
| 48. D776 | C2×C4 | semidirect |
| 49. #13095496 | C2×C4 | semidirect |
| 50. #13095496 | C2×C4 | semidirect |
| 51. C2×#11715895 | C2×C4 | semidirect |
| 52. C8×D97 | C2×C4 | semidirect |
| 53. C8×D97 | C2×C4 | semidirect |
| 56. C2×D4×C97 | C2×C4 | semidirect |
| 57. D8×C97 | C2×C4 | semidirect |
| 58. D8×C97 | C2×C4 | semidirect |
| 59. C2×C8×C97 | C2×C4 | semidirect |
| 109. C97 | #2948 | semidirect |
| 124. C2×D8 | #87604 | semidirect |
| 144. C2×D4 | C2×#87604 | semidirect |
| 151. D8 | C2×#87604 | semidirect |
| 152. D8 | C2×#87604 | semidirect |
| 161. C2×C8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261802 | 2 |
| #20261776 | 2 |
| D8×#87604 | 2 |
| #20261745 | 2 |
| #20261727 | 2 |
| #20261698 | 2 |
| C2×D8×D97 | 2 |
| #2948 | 97 |