Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 2. C2×#16837231 | C2 | semidirect |
| 4. #21425695 | C2 | semidirect |
| 5. #21425012 | C2 | semidirect |
| 7. C2×C59×#362 | C2 | semidirect |
| 12. C2×#14273670 | C4 | semidirect |
| 157. C2×#362 | D59 | semidirect |
| 187. C59 | #13246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273670 | 2 |
| C2×#16837231 | 2 |
| C2×#16837216 | 2 |
| #21425695 | 2 |
| #21425012 | 2 |
| #21425004 | 2 |
| C2×C59×#362 | 2 |
| #13246 | 59 |