Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D97 | C2 | semidirect |
| 2. C2×#15690842 | C2 | semidirect |
| 4. #20260890 | C2 | semidirect |
| 5. #20260889 | C2 | semidirect |
| 6. #20260876 | C2 | semidirect |
| 7. #20260875 | C2 | semidirect |
| 8. #20260874 | C2 | semidirect |
| 9. #20260742 | C2 | semidirect |
| 10. #20260697 | C2 | semidirect |
| 11. #451×C97 | C2 | semidirect |
| 23. C2×#13095501 | C22 | semidirect |
| 24. C2×#13095500 | C22 | semidirect |
| 25. C2×#13095498 | C22 | semidirect |
| 35. #15690735 | C22 | semidirect |
| 36. #15690734 | C22 | semidirect |
| 37. #15690733 | C22 | semidirect |
| 41. C2×Q16×C97 | C22 | semidirect |
| 43. #103×C97 | C22 | semidirect |
| 58. Q8×D97 | D4 | semidirect |
| 141. C22×C97 | #137 | semidirect |
| 152. C2×D97 | #137 | semidirect |
| 170. C97 | #3004 | semidirect |
| 176. #451 | D97 | semidirect |
| 195. C2×Q16 | C2×D97 | semidirect |
| 211. #103 | C2×D97 | semidirect |
| 321. C22 | #15690842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D97 | 2 |
| C2×#15690842 | 2 |
| #20261248 | 2 |
| #20260890 | 2 |
| #20260889 | 2 |
| #20260876 | 2 |
| #20260875 | 2 |
| #20260874 | 2 |
| #20260742 | 2 |
| #20260697 | 2 |
| #451×C97 | 2 |
| #3004 | 97 |