Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041994 | C2 | semidirect |
| 2. #26041629 | C2 | semidirect |
| 3. #26041617 | C2 | semidirect |
| 4. #26041569 | C2 | semidirect |
| 5. #26041510 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041424 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. D4×#13089678 | C2 | semidirect |
| 10. #26041275 | C2 | semidirect |
| 11. #547×C181 | C2 | semidirect |
| 130. C181 | #3303 | semidirect |
| 133. #547 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041629 | 2 |
| #26041617 | 2 |
| #26041569 | 2 |
| #26041510 | 2 |
| #26041481 | 2 |
| #26041424 | 2 |
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| #26041275 | 2 |
| #547×C181 | 2 |
| #3303 | 181 |