Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041824 | C2 | semidirect |
| 2. #26041568 | C2 | semidirect |
| 3. #26041567 | C2 | semidirect |
| 4. #26041532 | C2 | semidirect |
| 5. #26041530 | C2 | semidirect |
| 6. #26041473 | C2 | semidirect |
| 7. #26041472 | C2 | semidirect |
| 8. #26041302 | C2 | semidirect |
| 9. #469×C181 | C2 | semidirect |
| 112. C181 | #3253 | semidirect |
| 119. #469 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| #26041568 | 2 |
| #26041567 | 2 |
| #26041532 | 2 |
| #26041530 | 2 |
| #26041473 | 2 |
| #26041472 | 2 |
| #26041302 | 2 |
| #469×C181 | 2 |
| #3253 | 181 |