Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #26042002 | C2 | semidirect |
| 3. #26041629 | C2 | semidirect |
| 4. #26041619 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041517 | C2 | semidirect |
| 7. #26041440 | C2 | semidirect |
| 8. C4×#15668436 | C2 | semidirect |
| 9. #26041344 | C2 | semidirect |
| 10. #26041274 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 125. C181 | #3302 | semidirect |
| 133. #462 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041932 | 2 |
| #26041629 | 2 |
| #26041619 | 2 |
| #26041560 | 2 |
| #26041517 | 2 |
| #26041440 | 2 |
| C4×#15668436 | 2 |
| #26041344 | 2 |
| #26041274 | 2 |
| #462×C181 | 2 |
| #3302 | 181 |