Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20261082 | C2 | semidirect |
| 2. #20261025 | C2 | semidirect |
| 4. #20260486 | C2 | semidirect |
| 5. #20260483 | C2 | semidirect |
| 6. #20260478 | C2 | semidirect |
| 7. C8×D4×C97 | C2 | semidirect |
| 83. C97 | #1677 | semidirect |
| 87. C8×D4 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261082 | 2 |
| #20261025 | 2 |
| #20260930 | 2 |
| #20260486 | 2 |
| #20260483 | 2 |
| #20260478 | 2 |
| C8×D4×C97 | 2 |
| #1677 | 97 |