Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
204 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#16837242 | C2 | semidirect |
| 4. #21425954 | C2 | semidirect |
| 5. Dic59⋊C32 | C2 | semidirect |
| 7. C59×#1416 | C2 | semidirect |
| 95. #1416 | D59 | semidirect |
| 114. C59 | #13690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837242 | 2 |
| C2×#16837241 | 2 |
| #21426358 | 2 |
| #21425954 | 2 |
| Dic59⋊C32 | 2 |
| #21422273 | 2 |
| C59×#1416 | 2 |
| #13690 | 59 |