Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 2. #21425066 | C2 | semidirect |
| 4. #21424264 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C2×C59×#330 | C2 | semidirect |
| 206. C2×#330 | D59 | semidirect |
| 238. C59 | #10427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432146 | 2 |
| #21425066 | 2 |
| #21424912 | 2 |
| #21424264 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C2×C59×#330 | 2 |
| #10427 | 59 |