Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 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. #26042003 | C2 | semidirect |
| 3. #26041601 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041507 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041442 | C2 | semidirect |
| 8. C4×Dic724 | C2 | semidirect |
| 9. C8×D724 | C2 | semidirect |
| 10. #26041272 | C2 | semidirect |
| 11. #486×C181 | C2 | semidirect |
| 127. C181 | #3304 | semidirect |
| 131. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26041949 | 2 |
| #26041601 | 2 |
| #26041561 | 2 |
| #26041507 | 2 |
| #26041476 | 2 |
| #26041442 | 2 |
| C4×Dic724 | 2 |
| C8×D724 | 2 |
| #26041272 | 2 |
| #486×C181 | 2 |
| #3304 | 181 |