Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16837218 | C2 | semidirect |
| 4. #21425816 | C2 | semidirect |
| 5. #21425701 | C2 | semidirect |
| 6. #21424220 | C2 | semidirect |
| 24. C59×#495 | C4 | semidirect |
| 25. C59×#494 | C4 | semidirect |
| 183. #495 | Dic59 | semidirect |
| 184. #494 | Dic59 | semidirect |
| 195. C59 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837218 | 2 |
| #21425832 | 2 |
| #21425824 | 2 |
| #21425816 | 2 |
| #21425701 | 2 |
| #21424220 | 2 |
| C59×#3156 | 2 |
| #13216 | 59 |