Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
636 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21437245 | C2 | semidirect |
| 2. #21435900 | C2 | semidirect |
| 3. #21426218 | C2 | semidirect |
| 4. #21426174 | C2 | semidirect |
| 5. #21426073 | C2 | semidirect |
| 6. #21425978 | C2 | semidirect |
| 7. #21425934 | C2 | semidirect |
| 8. C59×#2247 | C2 | semidirect |
| 137. #2247 | D59 | semidirect |
| 169. C59 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437245 | 2 |
| #21435900 | 2 |
| #21426218 | 2 |
| #21426174 | 2 |
| #21426073 | 2 |
| #21425978 | 2 |
| #21425934 | 2 |
| C59×#2247 | 2 |
| #33860 | 59 |