Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic181 | C2 | semidirect |
| 3. C2×#19153742 | C2 | semidirect |
| 4. #26041252 | C2 | semidirect |
| 5. #26041050 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #421×C181 | C2 | semidirect |
| 10. #19153846 | C4 | semidirect |
| 12. #19153841 | C4 | semidirect |
| 33. C2×Dic362 | C2×C4 | semidirect |
| 34. C2×D724 | C2×C4 | semidirect |
| 44. #15668433 | C2×C4 | semidirect |
| 129. C181 | #1906 | semidirect |
| 133. #421 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| #41×Dic181 | 2 |
| C2×#19153742 | 2 |
| #26041252 | 2 |
| #26041050 | 2 |
| #26041038 | 2 |
| #421×C181 | 2 |
| #1906 | 181 |