Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26042075 | C2 | semidirect |
| 2. C2×#19153835 | C2 | semidirect |
| 3. #131×D181 | C2 | semidirect |
| 4. #26041555 | C2 | semidirect |
| 5. #26041554 | C2 | semidirect |
| 6. #26041546 | C2 | semidirect |
| 7. #26041541 | C2 | semidirect |
| 8. #26041540 | C2 | semidirect |
| 9. #108×D181 | C2 | semidirect |
| 10. #26041260 | C2 | semidirect |
| 11. #472×C181 | C2 | semidirect |
| 25. C2×Dic724 | C22 | semidirect |
| 26. C2×#15668437 | C22 | semidirect |
| 37. #19153752 | C22 | semidirect |
| 38. #19153751 | C22 | semidirect |
| 39. #19153734 | C22 | semidirect |
| 40. #19153734 | C22 | semidirect |
| 41. #19153733 | C22 | semidirect |
| 43. C2×D8×C181 | C22 | semidirect |
| 45. #108×C181 | C22 | semidirect |
| 46. #100×C181 | C22 | semidirect |
| 166. C181 | #3067 | semidirect |
| 174. #472 | D181 | semidirect |
| 195. C2×D8 | C2×D181 | semidirect |
| 209. #108 | C2×D181 | semidirect |
| 213. #100 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042075 | 2 |
| C2×#19153835 | 2 |
| #131×D181 | 2 |
| #26041555 | 2 |
| #26041554 | 2 |
| #26041546 | 2 |
| #26041541 | 2 |
| #26041540 | 2 |
| #108×D181 | 2 |
| #26041260 | 2 |
| #472×C181 | 2 |
| #3067 | 181 |