Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 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. C2×#19153875 | C2 | semidirect |
| 3. D181⋊#99 | C2 | semidirect |
| 4. #26042156 | C2 | semidirect |
| 17. #19153799 | C4 | semidirect |
| 21. #19153786 | C4 | semidirect |
| 22. #19153784 | C4 | semidirect |
| 24. #123×C181 | C4 | semidirect |
| 33. C22⋊#10624382 | D4 | semidirect |
| 35. C23×D181 | C2×C4 | semidirect |
| 52. C22⋊Dic181 | C2×C4 | semidirect |
| 58. C22×C4×C181 | C2×C4 | semidirect |
| 61. C22⋊C4×C181 | C2×C4 | semidirect |
| 135. C181 | #1913 | semidirect |
| 146. #123 | #10624382 | semidirect |
| 181. C22×C4 | C2×#10624382 | semidirect |
| 196. C22⋊C4 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042346 | 2 |
| C2×#19153875 | 2 |
| D181⋊#99 | 2 |
| #26042156 | 2 |
| #26041840 | 2 |
| #1913 | 181 |