Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 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. D181⋊(C22⋊C8) | C2 | semidirect |
| 2. C2×(C2×#10624382)⋊C4 | C2 | semidirect |
| 3. #26042131 | C2 | semidirect |
| 4. #26042130 | C2 | semidirect |
| 8. #19153873 | C22 | semidirect |
| 11. (C2×#10624382)⋊C4 | C22 | semidirect |
| 13. C2×D4×D181 | C4 | semidirect |
| 16. #19153790 | C4 | semidirect |
| 20. C4⋊C4×D181 | C4 | semidirect |
| 22. #121×C181 | C4 | semidirect |
| 32. C2×D724 | C2×C4 | semidirect |
| 46. C4⋊Dic181 | C2×C4 | semidirect |
| 52. C2×D4×C181 | C2×C4 | semidirect |
| 54. C4⋊C4×C181 | C2×C4 | semidirect |
| 130. D181 | #327 | semidirect |
| 131. C181 | C2×#327 | semidirect |
| 148. #121 | #10624382 | semidirect |
| 166. C2×D4 | C2×#10624382 | semidirect |
| 183. C4⋊C4 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C22⋊C8) | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| #26042131 | 2 |
| #26042130 | 2 |
| #121×D181 | 2 |
| C2×#327 | 181 |