Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041655 | C2 | semidirect |
| 3. #26041625 | C2 | semidirect |
| 4. #26041471 | C2 | semidirect |
| 5. #26041413 | C2 | semidirect |
| 6. #26041332 | C2 | semidirect |
| 7. C2×#127×C181 | C2 | semidirect |
| 9. C2×#15668434 | C22 | semidirect |
| 10. #19153816 | C22 | semidirect |
| 11. #19153813 | C22 | semidirect |
| 16. C4×D724 | C22 | semidirect |
| 17. C4⋊#13089678 | C22 | semidirect |
| 18. #19153737 | C22 | semidirect |
| 20. C4×#13089678 | C22 | semidirect |
| 81. C2×C4×C181 | D8 | semidirect |
| 112. C181 | #3205 | semidirect |
| 115. C2×#127 | D181 | semidirect |
| 193. C2×C4 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041655 | 2 |
| #26041625 | 2 |
| #26041471 | 2 |
| #26041413 | 2 |
| #26041332 | 2 |
| C2×#127×C181 | 2 |
| #3205 | 181 |