Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #21422861 | C2 | semidirect |
| 5. #21422691 | C2 | semidirect |
| 6. #21421969 | C2 | semidirect |
| 7. C59×#1559 | C2 | semidirect |
| 179. #1559 | D59 | semidirect |
| 211. C59 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435095 | 2 |
| #21424943 | 2 |
| #21422861 | 2 |
| #21422695 | 2 |
| #21422691 | 2 |
| #21421969 | 2 |
| C59×#1559 | 2 |
| #10498 | 59 |