Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
572 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21434670 | C2 | semidirect |
| 2. #21426242 | C2 | semidirect |
| 3. #21426241 | C2 | semidirect |
| 4. #21426199 | C2 | semidirect |
| 5. #21426197 | C2 | semidirect |
| 6. #21426130 | C2 | semidirect |
| 7. #21426129 | C2 | semidirect |
| 8. #21425851 | C2 | semidirect |
| 9. C59×#2218 | C2 | semidirect |
| 153. #2218 | D59 | semidirect |
| 187. C59 | #33819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434670 | 2 |
| #21426242 | 2 |
| #21426241 | 2 |
| #21426199 | 2 |
| #21426197 | 2 |
| #21426130 | 2 |
| #21426129 | 2 |
| #21425851 | 2 |
| C59×#2218 | 2 |
| #33819 | 59 |