Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #26041719 | C2 | semidirect |
| 2. C2×#19153760 | C2 | semidirect |
| 3. #26041554 | C2 | semidirect |
| 4. #26041092 | C2 | semidirect |
| 5. #26041086 | C2 | semidirect |
| 6. #26041063 | C2 | semidirect |
| 9. C2×Dic724 | C22 | semidirect |
| 13. #19153756 | C22 | semidirect |
| 14. C2×#15668424 | C22 | semidirect |
| 15. #19153752 | C22 | semidirect |
| 91. C181 | #2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041719 | 2 |
| C2×#19153760 | 2 |
| #26041554 | 2 |
| #26041092 | 2 |
| #26041086 | 2 |
| #26041063 | 2 |
| #576×C181 | 2 |
| #2194 | 181 |