Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16837231 | C2 | semidirect |
| 2. #21425856 | C2 | semidirect |
| 6. #21424879 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 142. #1387 | D59 | semidirect |
| 164. C59 | #13470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837231 | 2 |
| #21425856 | 2 |
| C2×#16837216 | 2 |
| C2×#16837202 | 2 |
| #21425004 | 2 |
| #21424879 | 2 |
| C59×#1387 | 2 |
| #13470 | 59 |