Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #21425715 | C2 | semidirect |
| 3. #21424145 | C2 | semidirect |
| 4. #21422091 | C2 | semidirect |
| 5. #21422089 | C2 | semidirect |
| 6. #21422087 | C2 | semidirect |
| 7. C59×#1341 | C2 | semidirect |
| 182. #1341 | D59 | semidirect |
| 208. C59 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433756 | 2 |
| #21425715 | 2 |
| #21424145 | 2 |
| #21422091 | 2 |
| #21422089 | 2 |
| #21422087 | 2 |
| C59×#1341 | 2 |
| #11872 | 59 |