Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26042079 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. #26041846 | C2 | semidirect |
| 4. #26041297 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041050 | C2 | semidirect |
| 7. #418×C181 | C2 | semidirect |
| 40. C2×Dic362 | D4 | semidirect |
| 42. C2×D724 | D4 | semidirect |
| 55. #15668433 | D4 | semidirect |
| 71. C2×C8×C181 | D4 | semidirect |
| 142. C181 | #2008 | semidirect |
| 148. #418 | D181 | semidirect |
| 210. C2×C8 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042079 | 2 |
| C2×#19153842 | 2 |
| #26041846 | 2 |
| #26041297 | 2 |
| #26041252 | 2 |
| #26041050 | 2 |
| #418×C181 | 2 |
| #2008 | 181 |