Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
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. #21439959 | C2 | semidirect |
| 2. #21439958 | C2 | semidirect |
| 3. #21439955 | C2 | semidirect |
| 4. #21439955 | C2 | semidirect |
| 5. #21439953 | C2 | semidirect |
| 6. #21439953 | C2 | semidirect |
| 7. #21439951 | C2 | semidirect |
| 8. #21439950 | C2 | semidirect |
| 12. #21439939 | C2 | semidirect |
| 13. #21439938 | C2 | semidirect |
| 14. #21439936 | C2 | semidirect |
| 15. C22⋊Q8×C239 | C2 | semidirect |
| 97. C239 | #563 | semidirect |
| 113. C22⋊Q8 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439959 | 2 |
| #21439958 | 2 |
| #21439955 | 2 |
| #21439953 | 2 |
| #21439951 | 2 |
| #21439950 | 2 |
| #21439946 | 2 |
| #21439943 | 2 |
| #21439942 | 2 |
| #21439939 | 2 |
| #21439938 | 2 |
| #21439936 | 2 |
| C22⋊Q8×C239 | 2 |
| #563 | 239 |