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 |
| 5. #26041562 | C2 | semidirect |
| 7. #26041486 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 9. #26041383 | C2 | semidirect |
| 11. #487×C181 | C2 | semidirect |
| 116. C181 | #3369 | semidirect |
| 121. #487 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042009 | 2 |
| #26042003 | 2 |
| #26041640 | 2 |
| #26041566 | 2 |
| #26041562 | 2 |
| #26041504 | 2 |
| #26041486 | 2 |
| #26041409 | 2 |
| #26041383 | 2 |
| C4×#15668438 | 2 |
| #487×C181 | 2 |
| #3369 | 181 |