Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041829 | C2 | semidirect |
| 2. #26041669 | C2 | semidirect |
| 3. #26041638 | C2 | semidirect |
| 4. #26041491 | C2 | semidirect |
| 5. #26041418 | C2 | semidirect |
| 6. #26041413 | C2 | semidirect |
| 7. #26041336 | C2 | semidirect |
| 8. C2×#124×C181 | C2 | semidirect |
| 10. C2×#15668436 | C22 | semidirect |
| 12. #19153816 | C22 | semidirect |
| 13. #19153813 | C22 | semidirect |
| 18. C4×D724 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 20. #19153740 | C22 | semidirect |
| 23. #19153727 | C22 | semidirect |
| 120. C181 | #3213 | semidirect |
| 123. C2×#124 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041669 | 2 |
| #26041638 | 2 |
| #26041491 | 2 |
| #26041418 | 2 |
| #26041413 | 2 |
| #26041336 | 2 |
| C2×#124×C181 | 2 |
| #3213 | 181 |