Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
830 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16837139 | C2 | semidirect |
| 5. #21422367 | C2 | semidirect |
| 6. #21421938 | C2 | semidirect |
| 7. C2×C59×#451 | C2 | semidirect |
| 238. C2×#451 | D59 | semidirect |
| 277. C59 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837541 | 2 |
| #21430030 | 2 |
| C2×#16837139 | 2 |
| C2×#16837137 | 2 |
| #21422367 | 2 |
| #21421938 | 2 |
| C2×C59×#451 | 2 |
| #9965 | 59 |