Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21435323 | C2 | semidirect |
| 2. #21434478 | C2 | semidirect |
| 3. #21423430 | C2 | semidirect |
| 4. #21423424 | C2 | semidirect |
| 5. #21423419 | C2 | semidirect |
| 6. #21422734 | C2 | semidirect |
| 7. #21422703 | C2 | semidirect |
| 238. C59 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435323 | 2 |
| #21434478 | 2 |
| #21423430 | 2 |
| #21423424 | 2 |
| #21423419 | 2 |
| #21422734 | 2 |
| #21422703 | 2 |
| C59×#3531 | 2 |
| #19005 | 59 |