Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21425695 | C2 | semidirect |
| 5. #21422185 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 7. C59×#2153 | C2 | semidirect |
| 137. #2153 | D59 | semidirect |
| 166. C59 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425725 | 2 |
| C2×#16837187 | 2 |
| #21425695 | 2 |
| #21423897 | 2 |
| #21422185 | 2 |
| #21422181 | 2 |
| C59×#2153 | 2 |
| #13123 | 59 |