Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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. #26042009 | C2 | semidirect |
| 4. #26041631 | C2 | semidirect |
| 5. #26041563 | C2 | semidirect |
| 7. #26041490 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041385 | C2 | semidirect |
| 116. C181 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042009 | 2 |
| #26041999 | 2 |
| #26041637 | 2 |
| #26041631 | 2 |
| #26041563 | 2 |
| #26041500 | 2 |
| #26041490 | 2 |
| #26041406 | 2 |
| #26041385 | 2 |
| C4×#15668437 | 2 |
| #476×C181 | 2 |
| #3369 | 181 |