Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
720 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21422714 | C2 | semidirect |
| 3. #21422557 | C2 | semidirect |
| 4. #21422430 | C2 | semidirect |
| 5. C59×#1750 | C2 | semidirect |
| 223. #1750 | D59 | semidirect |
| 258. C59 | #8349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437816 | 2 |
| #21422714 | 2 |
| #21422557 | 2 |
| #21422430 | 2 |
| C59×#1750 | 2 |
| #8349 | 59 |