Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26042007 | C2 | semidirect |
| 3. #26041651 | C2 | semidirect |
| 4. #26041650 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. #26041482 | C2 | semidirect |
| 7. #26041478 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 9. #26041370 | C2 | semidirect |
| 10. C4×#15668436 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 80. Dic362 | SD16 | semidirect |
| 92. #13089678 | #41 | semidirect |
| 128. C181 | #3392 | semidirect |
| 137. #460 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042007 | 2 |
| #26041949 | 2 |
| #26041651 | 2 |
| #26041650 | 2 |
| #26041485 | 2 |
| #26041482 | 2 |
| #26041478 | 2 |
| #26041403 | 2 |
| #26041370 | 2 |
| C4×#15668436 | 2 |
| #460×C181 | 2 |
| #3392 | 181 |