Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 368 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. #26041687 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041598 | C2 | semidirect |
| 6. #26041595 | C2 | semidirect |
| 7. #26041592 | C2 | semidirect |
| 8. #26041582 | C2 | semidirect |
| 9. #26041581 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #480×C181 | C2 | semidirect |
| 134. C181 | #3234 | semidirect |
| 143. #480 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×#19153807 | 2 |
| #26041687 | 2 |
| #26041642 | 2 |
| #26041598 | 2 |
| #26041595 | 2 |
| #26041592 | 2 |
| #26041582 | 2 |
| #26041581 | 2 |
| #26041333 | 2 |
| #480×C181 | 2 |
| #3234 | 181 |