Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #26041241 | C2 | semidirect |
| 3. #95×D181 | C2 | semidirect |
| 4. #26041017 | C2 | semidirect |
| 5. #26041015 | C2 | semidirect |
| 6. #26041013 | C2 | semidirect |
| 7. #327×C181 | C2 | semidirect |
| 8. C2×#15668448 | C4 | semidirect |
| 13. #19153796 | C4 | semidirect |
| 15. #19153787 | C4 | semidirect |
| 19. #19153774 | C4 | semidirect |
| 29. C2×Dic362 | C2×C4 | semidirect |
| 46. C4⋊Dic181 | C2×C4 | semidirect |
| 54. C2×D4×C181 | C2×C4 | semidirect |
| 58. C4⋊C4×C181 | C2×C4 | semidirect |
| 130. C181 | #1504 | semidirect |
| 138. #327 | D181 | semidirect |
| 164. C2×D4 | C4×D181 | semidirect |
| 184. C4⋊C4 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041789 | 2 |
| #26041241 | 2 |
| #95×D181 | 2 |
| #26041017 | 2 |
| #26041015 | 2 |
| #26041013 | 2 |
| #327×C181 | 2 |
| #1504 | 181 |