Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #26042004 | C2 | semidirect |
| 3. #26041632 | C2 | semidirect |
| 4. #26041577 | C2 | semidirect |
| 5. #26041561 | C2 | semidirect |
| 6. #26041500 | C2 | semidirect |
| 8. C8×Dic362 | C2 | semidirect |
| 9. C4×Dic724 | C2 | semidirect |
| 10. #26041370 | C2 | semidirect |
| 117. C181 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042015 | 2 |
| #26042004 | 2 |
| #26041632 | 2 |
| #26041577 | 2 |
| #26041561 | 2 |
| #26041500 | 2 |
| #26041476 | 2 |
| C8×Dic362 | 2 |
| C4×Dic724 | 2 |
| #26041370 | 2 |
| #486×C181 | 2 |
| #3365 | 181 |