Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15690834 | C2 | semidirect |
| 2. #20261283 | C2 | semidirect |
| 3. C4×D4×D97 | C2 | semidirect |
| 4. #20260949 | C2 | semidirect |
| 5. #20260948 | C2 | semidirect |
| 6. #20260941 | C2 | semidirect |
| 7. #20260940 | C2 | semidirect |
| 8. #20260927 | C2 | semidirect |
| 9. #20260757 | C2 | semidirect |
| 10. #20260733 | C2 | semidirect |
| 11. #459×C97 | C2 | semidirect |
| 20. #15690810 | C22 | semidirect |
| 21. #15690797 | C22 | semidirect |
| 34. C4⋊#11715895 | C22 | semidirect |
| 35. #15690739 | C22 | semidirect |
| 36. #15690735 | C22 | semidirect |
| 37. #15690733 | C22 | semidirect |
| 38. #15690731 | C22 | semidirect |
| 40. #127×C97 | C22 | semidirect |
| 42. C4⋊C8×C97 | C22 | semidirect |
| 43. #102×C97 | C22 | semidirect |
| 52. D4×D97 | D4 | semidirect |
| 145. C4×C97 | AGL(1,ℤ/8) | semidirect |
| 161. C97 | #3036 | semidirect |
| 170. #459 | D97 | semidirect |
| 183. #127 | C2×D97 | semidirect |
| 200. C4⋊C8 | C2×D97 | semidirect |
| 204. #102 | C2×D97 | semidirect |
| 311. C4 | #15690834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690834 | 2 |
| #20261283 | 2 |
| C4×D4×D97 | 2 |
| #20260949 | 2 |
| #20260948 | 2 |
| #20260941 | 2 |
| #20260940 | 2 |
| #20260927 | 2 |
| #20260757 | 2 |
| #20260733 | 2 |
| #459×C97 | 2 |
| #3036 | 97 |