Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #26042004 | C2 | semidirect |
| 3. #26041672 | C2 | semidirect |
| 5. #26041503 | C2 | semidirect |
| 6. #26041483 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041382 | C2 | semidirect |
| 10. C4×#15668439 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 121. C181 | #3400 | semidirect |
| 128. #462 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| #26042004 | 2 |
| #26041672 | 2 |
| #26041653 | 2 |
| #26041503 | 2 |
| #26041483 | 2 |
| #26041480 | 2 |
| #26041406 | 2 |
| #26041382 | 2 |
| C4×#15668439 | 2 |
| #462×C181 | 2 |
| #3400 | 181 |