Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26041302 | C2 | semidirect |
| 5. C4×#15668428 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #339×C181 | C2 | semidirect |
| 10. #19153781 | C4 | semidirect |
| 11. #19153781 | C4 | semidirect |
| 12. #19153778 | C4 | semidirect |
| 13. #19153778 | C4 | semidirect |
| 71. Dic362 | C4⋊C4 | semidirect |
| 73. D724 | C4⋊C4 | semidirect |
| 124. Dic181 | #104 | semidirect |
| 131. C181 | #1806 | semidirect |
| 139. #339 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041747 | 2 |
| #26041302 | 2 |
| C2×#19153744 | 2 |
| C2×#19153742 | 2 |
| C4×#15668428 | 2 |
| #26041038 | 2 |
| #339×C181 | 2 |
| #1806 | 181 |