Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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. Q8×Dic362 | C2 | semidirect |
| 2. #26041638 | C2 | semidirect |
| 4. #26041574 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 6. #26041498 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 9. #26041379 | C2 | semidirect |
| 10. C4×#15668439 | C2 | semidirect |
| 118. C181 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26041638 | 2 |
| #26041625 | 2 |
| #26041574 | 2 |
| #26041559 | 2 |
| #26041498 | 2 |
| #26041476 | 2 |
| #26041410 | 2 |
| #26041379 | 2 |
| C4×#15668439 | 2 |
| #559×C181 | 2 |
| #3375 | 181 |