Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
878 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 159 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. #21425832 | C2 | semidirect |
| 2. #21425816 | C2 | semidirect |
| 3. #21425717 | C2 | semidirect |
| 4. #21424142 | C2 | semidirect |
| 18. C2×#135×C59 | C4 | semidirect |
| 20. C22×Q16×C59 | C4 | semidirect |
| 179. C2×#135 | Dic59 | semidirect |
| 181. C22×Q16 | Dic59 | semidirect |
| 191. C59 | #12742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425832 | 2 |
| #21425816 | 2 |
| #21425717 | 2 |
| #21424142 | 2 |
| C2×C59×#578 | 2 |
| #12742 | 59 |