Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #20261431 | C2 | semidirect |
| 2. #20261137 | C2 | semidirect |
| 3. #20261060 | C2 | semidirect |
| 4. #20261049 | C2 | semidirect |
| 5. #20261036 | C2 | semidirect |
| 6. #20260988 | C2 | semidirect |
| 7. C4×D776 | C2 | semidirect |
| 8. #20260777 | C2 | semidirect |
| 9. #436×C97 | C2 | semidirect |
| 103. C97 | #3355 | semidirect |
| 111. #436 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261431 | 2 |
| #20261137 | 2 |
| #20261060 | 2 |
| #20261049 | 2 |
| #20261036 | 2 |
| #20260988 | 2 |
| C4×D776 | 2 |
| #20260777 | 2 |
| #436×C97 | 2 |
| #3355 | 97 |