Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13095496 | C2 | semidirect |
| 2. C2×#15690818 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20261302 | C2 | semidirect |
| 5. #20260987 | C2 | semidirect |
| 6. #20260970 | C2 | semidirect |
| 7. #20260771 | C2 | semidirect |
| 8. #20260741 | C2 | semidirect |
| 9. #418×C97 | C2 | semidirect |
| 16. C2×#13095494 | C22 | semidirect |
| 18. C2×C8×D97 | C22 | semidirect |
| 23. #15690785 | C22 | semidirect |
| 24. #15690781 | C22 | semidirect |
| 28. #15690743 | C22 | semidirect |
| 29. #15690741 | C22 | semidirect |
| 30. #15690732 | C22 | semidirect |
| 34. #102×C97 | C22 | semidirect |
| 51. C2×#11715895 | D4 | semidirect |
| 126. C97 | #3058 | semidirect |
| 135. #418 | D97 | semidirect |
| 160. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×#15690818 | 2 |
| #20261304 | 2 |
| #20261302 | 2 |
| #20260987 | 2 |
| #20260970 | 2 |
| #20260771 | 2 |
| #20260741 | 2 |
| #418×C97 | 2 |
| #3058 | 97 |