Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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. C4⋊C8×Dic59 | C2 | semidirect |
| 4. #21421979 | C2 | semidirect |
| 5. C59×#1296 | C2 | semidirect |
| 15. #16837145 | C4 | semidirect |
| 35. C4⋊(C59⋊C8) | C2×C4 | semidirect |
| 42. C4⋊C8×C59 | C2×C4 | semidirect |
| 136. Dic59 | #331 | semidirect |
| 141. #1296 | D59 | semidirect |
| 160. C59 | C4×#331 | semidirect |
| 184. C4⋊C8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426658 | 2 |
| C4⋊C8×Dic59 | 2 |
| C2×#16837145 | 2 |
| #21421979 | 2 |
| C59×#1296 | 2 |
| C4×#331 | 59 |