Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#19153842 | C2 | semidirect |
| 2. #26041848 | C2 | semidirect |
| 3. C2×#19153812 | C2 | semidirect |
| 4. C2×#19153742 | C2 | semidirect |
| 5. C2×#19153732 | C2 | semidirect |
| 6. #26041038 | C2 | semidirect |
| 7. #418×C181 | C2 | semidirect |
| 34. C2×Dic362 | D4 | semidirect |
| 42. C2×D724 | D4 | semidirect |
| 51. #15668433 | D4 | semidirect |
| 55. C4×Dic181 | D4 | semidirect |
| 62. C2×D4×C181 | D4 | semidirect |
| 67. C4⋊C4×C181 | D4 | semidirect |
| 138. C181 | #2002 | semidirect |
| 144. #418 | D181 | semidirect |
| 191. C2×D4 | D724 | semidirect |
| 203. C4⋊C4 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| #26041848 | 2 |
| C2×#19153812 | 2 |
| C2×#19153742 | 2 |
| C2×#19153732 | 2 |
| #26041038 | 2 |
| #418×C181 | 2 |
| #2002 | 181 |