Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041759 | C2 | semidirect |
| 3. #26041606 | C2 | semidirect |
| 4. #26041605 | C2 | semidirect |
| 5. #26041599 | C2 | semidirect |
| 6. #26041594 | C2 | semidirect |
| 7. #26041322 | C2 | semidirect |
| 8. #26041283 | C2 | semidirect |
| 9. C2×#19153738 | C2 | semidirect |
| 10. #26041245 | C2 | semidirect |
| 11. #427×C181 | C2 | semidirect |
| 23. #19153774 | C22 | semidirect |
| 25. C4⋊C4×D181 | C22 | semidirect |
| 26. #19153749 | C22 | semidirect |
| 27. #19153747 | C22 | semidirect |
| 32. #19153728 | C22 | semidirect |
| 33. #19153728 | C22 | semidirect |
| 37. #107×C181 | C22 | semidirect |
| 38. #107×C181 | C22 | semidirect |
| 39. #106×C181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 134. C181 | #3096 | semidirect |
| 143. #427 | D181 | semidirect |
| 165. #107 | C2×D181 | semidirect |
| 166. #107 | C2×D181 | semidirect |
| 168. #106 | C2×D181 | semidirect |
| 169. #106 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041848 | 2 |
| #26041759 | 2 |
| #26041606 | 2 |
| #26041605 | 2 |
| #26041599 | 2 |
| #26041594 | 2 |
| #26041322 | 2 |
| #26041283 | 2 |
| C2×#19153738 | 2 |
| #26041245 | 2 |
| #427×C181 | 2 |
| #3096 | 181 |