Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21439950 | C2 | semidirect |
| 6. Q8×Dic239 | C2 | semidirect |
| 7. #21439925 | C2 | semidirect |
| 8. #21439925 | C2 | semidirect |
| 38. C2×Dic239 | Q8 | semidirect |
| 70. C239 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439959 | 2 |
| #21439958 | 2 |
| #21439950 | 2 |
| #21439939 | 2 |
| #21439937 | 2 |
| Q8×Dic239 | 2 |
| #21439925 | 2 |
| #21439916 | 2 |
| C2×C4×Dic239 | 2 |
| C22⋊Q8×C239 | 2 |
| #533 | 239 |