Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19153807 | C2 | semidirect |
| 3. #26041679 | C2 | semidirect |
| 4. #26041635 | C2 | semidirect |
| 5. #26041612 | C2 | semidirect |
| 8. #26041584 | C2 | semidirect |
| 9. #26041578 | C2 | semidirect |
| 10. #26041329 | C2 | semidirect |
| 11. #483×C181 | C2 | semidirect |
| 125. C181 | #3232 | semidirect |
| 132. #483 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041815 | 2 |
| C2×#19153807 | 2 |
| #26041679 | 2 |
| #26041635 | 2 |
| #26041612 | 2 |
| #26041598 | 2 |
| #26041592 | 2 |
| #26041584 | 2 |
| #26041578 | 2 |
| #26041329 | 2 |
| #483×C181 | 2 |
| #3232 | 181 |