Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #20261021 | C2 | semidirect |
| 5. #20261020 | C2 | semidirect |
| 6. #20260942 | C2 | semidirect |
| 8. #20260842 | C2 | semidirect |
| 9. #20260839 | C2 | semidirect |
| 11. #462×C97 | C2 | semidirect |
| 133. C97 | #3113 | semidirect |
| 140. #462 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4×Q8×D97 | 2 |
| #20261064 | 2 |
| #20261021 | 2 |
| #20261020 | 2 |
| #20260942 | 2 |
| #20260889 | 2 |
| #20260842 | 2 |
| #20260839 | 2 |
| #20260791 | 2 |
| #462×C97 | 2 |
| #3113 | 97 |