Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#16837226 | C2 | semidirect |
| 5. #21422195 | C2 | semidirect |
| 6. #21422194 | C2 | semidirect |
| 7. C2×C59×#365 | C2 | semidirect |
| 18. (C2×D59)⋊C16 | C4 | semidirect |
| 142. C2×#365 | D59 | semidirect |
| 168. C59 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837437 | 2 |
| C2×#16837226 | 2 |
| #21425706 | 2 |
| #21424131 | 2 |
| #21422195 | 2 |
| #21422194 | 2 |
| C2×C59×#365 | 2 |
| #12930 | 59 |