Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041884 | C2 | semidirect |
| 2. #26041579 | C2 | semidirect |
| 3. #26041576 | C2 | semidirect |
| 4. #26041530 | C2 | semidirect |
| 5. #26041513 | C2 | semidirect |
| 6. #26041474 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041306 | C2 | semidirect |
| 9. #540×C181 | C2 | semidirect |
| 106. C181 | #3259 | semidirect |
| 109. #540 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041884 | 2 |
| #26041579 | 2 |
| #26041576 | 2 |
| #26041530 | 2 |
| #26041513 | 2 |
| #26041474 | 2 |
| #26041471 | 2 |
| #26041306 | 2 |
| #540×C181 | 2 |
| #3259 | 181 |