Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21435437 | C2 | semidirect |
| 4. #21422109 | C2 | semidirect |
| 5. #21422108 | C2 | semidirect |
| 6. #21422035 | C2 | semidirect |
| 140. C2×Dic59 | SD32 | semidirect |
| 202. C59 | #12159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435437 | 2 |
| #21426025 | 2 |
| #21425404 | 2 |
| #21422109 | 2 |
| #21422108 | 2 |
| #21422035 | 2 |
| C59×#2187 | 2 |
| #12159 | 59 |