Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20261457 | C2 | semidirect |
| 2. #20261128 | C2 | semidirect |
| 4. #20260957 | C2 | semidirect |
| 6. #20260944 | C2 | semidirect |
| 7. #20260865 | C2 | semidirect |
| 8. #20260834 | C2 | semidirect |
| 9. C4×Q16×C97 | C2 | semidirect |
| 103. C97 | #3402 | semidirect |
| 112. C4×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261457 | 2 |
| #20261128 | 2 |
| #20261119 | 2 |
| #20260957 | 2 |
| #20260953 | 2 |
| #20260944 | 2 |
| #20260865 | 2 |
| #20260834 | 2 |
| C4×Q16×C97 | 2 |
| #3402 | 97 |