Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
404 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21432284 | C2 | semidirect |
| 4. #21422116 | C2 | semidirect |
| 5. #21422095 | C2 | semidirect |
| 6. #21422044 | C2 | semidirect |
| 222. C59 | #12139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432284 | 2 |
| #21423082 | 2 |
| #21423048 | 2 |
| #21422116 | 2 |
| #21422095 | 2 |
| #21422044 | 2 |
| C59×#2044 | 2 |
| #12139 | 59 |