Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #26042250 | C2 | semidirect |
| 2. C2×(C2×#10624382)⋊C4 | C2 | semidirect |
| 3. #26042133 | C2 | semidirect |
| 4. #26042131 | C2 | semidirect |
| 12. C2×#15668450 | C4 | semidirect |
| 17. #19153790 | C4 | semidirect |
| 21. #19153774 | C4 | semidirect |
| 22. C22⋊Q8×C181 | C4 | semidirect |
| 33. C2×D724 | C2×C4 | semidirect |
| 42. C4⋊Dic181 | C2×C4 | semidirect |
| 49. C2×Q8×C181 | C2×C4 | semidirect |
| 52. C4⋊C4×C181 | C2×C4 | semidirect |
| 119. C181 | #1504 | semidirect |
| 132. C22⋊Q8 | #10624382 | semidirect |
| 145. C2×Q8 | C2×#10624382 | semidirect |
| 167. C4⋊C4 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042250 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| #26042133 | 2 |
| #26042131 | 2 |
| #26041792 | 2 |
| #1504 | 181 |