Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1916 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1916 conjugacy classes of subgroups — too many to draw. Only its 287 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×#16838202 | C2 | semidirect |
| 2. #21432540 | C2 | semidirect |
| 3. #21425201 | C2 | semidirect |
| 4. C2×C59×#338 | C2 | semidirect |
| 8. #16838202 | C22 | semidirect |
| 13. #16837370 | C22 | semidirect |
| 17. C59×#338 | C22 | semidirect |
| 145. C2×#338 | D59 | semidirect |
| 163. #338 | C2×D59 | semidirect |
| 164. C59 | #23434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838202 | 2 |
| #21432540 | 2 |
| #21425201 | 2 |
| C2×C59×#338 | 2 |
| #23434 | 59 |