Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #26041934 | C2 | semidirect |
| 2. #26041631 | C2 | semidirect |
| 3. #26041620 | C2 | semidirect |
| 4. #26041566 | C2 | semidirect |
| 5. #26041506 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 7. #26041422 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. #26041273 | C2 | semidirect |
| 11. #555×C181 | C2 | semidirect |
| 130. C181 | #3303 | semidirect |
| 132. #555 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041934 | 2 |
| #26041631 | 2 |
| #26041620 | 2 |
| #26041566 | 2 |
| #26041506 | 2 |
| #26041484 | 2 |
| #26041422 | 2 |
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| #26041273 | 2 |
| #555×C181 | 2 |
| #3303 | 181 |