Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26044260 | C2 | semidirect |
| 2. #26044259 | C2 | semidirect |
| 3. #26044256 | C2 | semidirect |
| 4. #26044256 | C2 | semidirect |
| 5. #26044254 | C2 | semidirect |
| 6. #26044254 | C2 | semidirect |
| 7. #26044252 | C2 | semidirect |
| 8. #26044251 | C2 | semidirect |
| 12. #26044240 | C2 | semidirect |
| 13. #26044239 | C2 | semidirect |
| 14. #26044237 | C2 | semidirect |
| 15. C22⋊Q8×C367 | C2 | semidirect |
| 97. C367 | #563 | semidirect |
| 113. C22⋊Q8 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044260 | 2 |
| #26044259 | 2 |
| #26044256 | 2 |
| #26044254 | 2 |
| #26044252 | 2 |
| #26044251 | 2 |
| #26044247 | 2 |
| #26044244 | 2 |
| #26044243 | 2 |
| #26044240 | 2 |
| #26044239 | 2 |
| #26044237 | 2 |
| C22⋊Q8×C367 | 2 |
| #563 | 367 |