Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3294 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 667 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. #21432360 | C2 | direct (N × H) |
| 2. C2×#16837338 | C2 | semidirect |
| 3. C2×#16837325 | C2 | semidirect |
| 6. C22×C4⋊Dic59 | C22 | semidirect |
| 7. C22×Dic59⋊C4 | C22 | semidirect |
| 11. #16837338 | C22 | semidirect |
| 12. #16837325 | C22 | semidirect |
| 14. C2×C59⋊#95 | C22 | semidirect |
| 21. C2×C4⋊Dic59 | C23 | semidirect |
| 23. C2×Dic59⋊C4 | C23 | semidirect |
| 30. C59⋊#95 | C23 | semidirect |
| 127. C2×C59 | #2842 | semidirect |
| 144. C59 | C2×#2842 | semidirect |
| 247. C2 | #21432360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432360 | 2 |
| C2×#16837338 | 2 |
| C2×#16837325 | 2 |
| C2×#16837258 | 2 |
| C2×C59×#379 | 2 |
| C2×#2842 | 59 |