Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041985 | C2 | semidirect |
| 2. #26041683 | C2 | semidirect |
| 3. #26041680 | C2 | semidirect |
| 4. #26041578 | C2 | semidirect |
| 5. #26041576 | C2 | semidirect |
| 6. #26041568 | C2 | semidirect |
| 7. C8×Dic362 | C2 | semidirect |
| 11. #499×C181 | C2 | semidirect |
| 45. D1448 | Q8 | semidirect |
| 108. C181 | #3380 | semidirect |
| 113. #499 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041985 | 2 |
| #26041683 | 2 |
| #26041680 | 2 |
| #26041578 | 2 |
| #26041576 | 2 |
| #26041568 | 2 |
| C8×Dic362 | 2 |
| C4×D1448 | 2 |
| #26041361 | 2 |
| #499×C181 | 2 |
| #3380 | 181 |