Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
914 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21425846 | C2 | semidirect |
| 3. #21425825 | C2 | semidirect |
| 4. #21424138 | C2 | semidirect |
| 5. C2×C59×#349 | C2 | semidirect |
| 14. C2×#14273663 | C22 | semidirect |
| 15. C2×#14273663 | C22 | semidirect |
| 22. C2×M32×C59 | C22 | semidirect |
| 190. C2×#349 | D59 | semidirect |
| 207. C2×M32 | C2×D59 | semidirect |
| 216. C59 | #12740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838202 | 2 |
| #21425846 | 2 |
| #21425825 | 2 |
| #21424138 | 2 |
| C2×C59×#349 | 2 |
| #12740 | 59 |