Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #21432964 | C2 | semidirect |
| 4. #21426160 | C2 | semidirect |
| 5. #21426144 | C2 | semidirect |
| 6. #21425854 | C2 | semidirect |
| 7. #21425816 | C2 | semidirect |
| 9. C22×Q32×C59 | C2 | semidirect |
| 169. C22×Q32 | D59 | semidirect |
| 206. C59 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| #21434585 | 2 |
| #21432964 | 2 |
| #21426160 | 2 |
| #21426144 | 2 |
| #21425854 | 2 |
| #21425816 | 2 |
| #21425804 | 2 |
| C22×Q32×C59 | 2 |
| #33588 | 59 |