Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26042346 | C2 | semidirect |
| 2. #26042278 | C2 | semidirect |
| 3. D181⋊#100 | C2 | semidirect |
| 4. #26042146 | C2 | semidirect |
| 14. #19153813 | C4 | semidirect |
| 15. #19153812 | C4 | semidirect |
| 16. #19153805 | C4 | semidirect |
| 20. #124×C181 | C4 | semidirect |
| 28. C4×#10624382 | D4 | semidirect |
| 35. C2×D724 | C2×C4 | semidirect |
| 45. C4×Dic181 | C2×C4 | semidirect |
| 46. C2×Q8×C181 | C2×C4 | semidirect |
| 49. C42×C181 | C2×C4 | semidirect |
| 102. C181 | #1911 | semidirect |
| 115. #124 | #10624382 | semidirect |
| 127. C2×Q8 | C2×#10624382 | semidirect |
| 152. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042346 | 2 |
| #26042278 | 2 |
| D181⋊#100 | 2 |
| #26042146 | 2 |
| #26041847 | 2 |
| #1911 | 181 |