Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 9. #19153815 | C4 | semidirect |
| 10. #19153807 | C4 | semidirect |
| 37. C4×Dic181 | Q8 | semidirect |
| 47. C42×C181 | Q8 | semidirect |
| 85. C181 | #1995 | semidirect |
| 133. C42 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041832 | 2 |
| #26041302 | 2 |
| #26041125 | 2 |
| #26041040 | 2 |
| #26041039 | 2 |
| #26041038 | 2 |
| #339×C181 | 2 |
| #1995 | 181 |