Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#15690831 | C2 | semidirect |
| 2. #20261389 | C2 | semidirect |
| 3. #20261388 | C2 | semidirect |
| 4. #20261114 | C2 | semidirect |
| 5. #20260975 | C2 | semidirect |
| 6. #20260941 | C2 | semidirect |
| 7. #20260900 | C2 | semidirect |
| 8. #20260894 | C2 | semidirect |
| 9. C4×#13095496 | C2 | semidirect |
| 10. #20260800 | C2 | semidirect |
| 11. #461×C97 | C2 | semidirect |
| 58. #13095496 | D4 | semidirect |
| 126. C4×C97 | #135 | semidirect |
| 139. C97 | #3283 | semidirect |
| 146. #461 | D97 | semidirect |
| 268. C4 | #15690831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| #20261389 | 2 |
| #20261388 | 2 |
| #20261114 | 2 |
| #20260975 | 2 |
| #20260941 | 2 |
| #20260900 | 2 |
| #20260894 | 2 |
| C4×#13095496 | 2 |
| #20260800 | 2 |
| #461×C97 | 2 |
| #3283 | 97 |