Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 216 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×#16837239 | C2 | semidirect |
| 3. #21426358 | C2 | semidirect |
| 4. #21425942 | C2 | semidirect |
| 5. Dic59⋊C32 | C2 | semidirect |
| 6. #21422273 | C2 | semidirect |
| 7. C59×#1416 | C2 | semidirect |
| 98. #1416 | D59 | semidirect |
| 118. C59 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837239 | 2 |
| C2×D1888 | 2 |
| #21426358 | 2 |
| #21425942 | 2 |
| Dic59⋊C32 | 2 |
| #21422273 | 2 |
| C59×#1416 | 2 |
| #13689 | 59 |