Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21424236 | C2 | semidirect |
| 5. #21421954 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#1286 | C2 | semidirect |
| 147. #1286 | D59 | semidirect |
| 168. C59 | #10634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424919 | 2 |
| #21424236 | 2 |
| #21422765 | 2 |
| #21422763 | 2 |
| #21421954 | 2 |
| #21421940 | 2 |
| C59×#1286 | 2 |
| #10634 | 59 |