Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 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. #26041985 | C2 | semidirect |
| 2. #26041686 | C2 | semidirect |
| 3. #26041582 | C2 | semidirect |
| 4. #26041576 | C2 | semidirect |
| 5. #26041558 | C2 | semidirect |
| 6. #26041409 | C2 | semidirect |
| 9. #499×C181 | C2 | semidirect |
| 41. D1448 | Q8 | semidirect |
| 96. C181 | #3389 | semidirect |
| 100. #499 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041985 | 2 |
| #26041686 | 2 |
| #26041582 | 2 |
| #26041576 | 2 |
| #26041558 | 2 |
| #26041409 | 2 |
| #26041390 | 2 |
| C4×D1448 | 2 |
| #499×C181 | 2 |
| #3389 | 181 |