Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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. #26041357 | C2 | semidirect |
| 2. #26041351 | C2 | semidirect |
| 3. #26041340 | C2 | semidirect |
| 4. #26041246 | C2 | semidirect |
| 5. #26041243 | C2 | semidirect |
| 8. C2×#15668433 | C22 | semidirect |
| 9. C22×#13089678 | C22 | semidirect |
| 10. C4⋊#13089678 | C22 | semidirect |
| 14. C22⋊#13089678 | C22 | semidirect |
| 15. #19153727 | C22 | semidirect |
| 16. C4×#13089678 | C22 | semidirect |
| 89. C181 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041357 | 2 |
| #26041351 | 2 |
| #26041340 | 2 |
| #26041246 | 2 |
| #26041243 | 2 |
| #525×C181 | 2 |
| #2978 | 181 |