Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. #26041829 | C2 | semidirect |
| 3. #26041666 | C2 | semidirect |
| 4. #26041655 | C2 | semidirect |
| 5. #26041651 | C2 | semidirect |
| 6. C4×#15668433 | C2 | semidirect |
| 7. C2×#127×C181 | C2 | semidirect |
| 10. C2×#15668437 | C22 | semidirect |
| 11. C2×#15668434 | C22 | semidirect |
| 13. #19153816 | C22 | semidirect |
| 14. #19153813 | C22 | semidirect |
| 15. #19153804 | C22 | semidirect |
| 18. #19153727 | C22 | semidirect |
| 19. C4×#13089678 | C22 | semidirect |
| 34. #15668433 | D4 | semidirect |
| 57. #13089678 | C2×D4 | semidirect |
| 82. C4×C181 | AGL(1,ℤ/8) | semidirect |
| 90. C181 | #3151 | semidirect |
| 94. C2×#127 | D181 | semidirect |
| 174. C4 | #19153842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153842 | 2 |
| #26041829 | 2 |
| #26041666 | 2 |
| #26041655 | 2 |
| #26041651 | 2 |
| C4×#15668433 | 2 |
| C2×#127×C181 | 2 |
| #3151 | 181 |