Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
182 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20260941 | C2 | semidirect |
| 4. C8×D388 | C2 | semidirect |
| 5. #20260482 | C2 | semidirect |
| 6. #20260478 | C2 | semidirect |
| 7. #335×C97 | C2 | semidirect |
| 85. C97 | #1681 | semidirect |
| 90. #335 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261082 | 2 |
| #20260941 | 2 |
| #20260931 | 2 |
| C8×D388 | 2 |
| #20260482 | 2 |
| #20260478 | 2 |
| #335×C97 | 2 |
| #1681 | 97 |