Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21434739 | C2 | semidirect |
| 2. #21426256 | C2 | semidirect |
| 3. #21426251 | C2 | semidirect |
| 4. #21426197 | C2 | semidirect |
| 5. #21426182 | C2 | semidirect |
| 6. #21426130 | C2 | semidirect |
| 7. #21426129 | C2 | semidirect |
| 8. #21425854 | C2 | semidirect |
| 9. C59×#2215 | C2 | semidirect |
| 151. #2215 | D59 | semidirect |
| 186. C59 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434739 | 2 |
| #21426256 | 2 |
| #21426251 | 2 |
| #21426197 | 2 |
| #21426182 | 2 |
| #21426130 | 2 |
| #21426129 | 2 |
| #21425854 | 2 |
| C59×#2215 | 2 |
| #33825 | 59 |