Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21425861 | C2 | semidirect |
| 5. #21424221 | C2 | semidirect |
| 6. #21422197 | C2 | semidirect |
| 7. C59×#1389 | C2 | semidirect |
| 11. #16837513 | C4 | semidirect |
| 138. #1389 | D59 | semidirect |
| 161. C59 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432947 | 2 |
| #21425861 | 2 |
| C2×#16837214 | 2 |
| #21425813 | 2 |
| #21424221 | 2 |
| #21422197 | 2 |
| C59×#1389 | 2 |
| #12826 | 59 |