Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 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. #26041999 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041667 | C2 | semidirect |
| 4. #26041651 | C2 | semidirect |
| 5. #26041492 | C2 | semidirect |
| 6. #26041485 | C2 | semidirect |
| 7. #26041478 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. C4×#15668434 | C2 | semidirect |
| 11. #459×C181 | C2 | semidirect |
| 92. #13089678 | #41 | semidirect |
| 132. C181 | #3397 | semidirect |
| 141. #459 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| #26041949 | 2 |
| #26041667 | 2 |
| #26041651 | 2 |
| #26041492 | 2 |
| #26041485 | 2 |
| #26041478 | 2 |
| #26041406 | 2 |
| #26041376 | 2 |
| C4×#15668434 | 2 |
| #459×C181 | 2 |
| #3397 | 181 |