Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19153808 | C2 | semidirect |
| 3. #26041681 | C2 | semidirect |
| 4. #26041634 | C2 | semidirect |
| 5. #26041615 | C2 | semidirect |
| 6. #26041610 | C2 | semidirect |
| 9. #26041587 | C2 | semidirect |
| 10. #26041580 | C2 | semidirect |
| 11. #431×C181 | C2 | semidirect |
| 125. C181 | #3232 | semidirect |
| 137. #431 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| C2×#19153808 | 2 |
| #26041681 | 2 |
| #26041634 | 2 |
| #26041615 | 2 |
| #26041610 | 2 |
| #26041598 | 2 |
| #26041593 | 2 |
| #26041587 | 2 |
| #26041580 | 2 |
| #431×C181 | 2 |
| #3232 | 181 |