Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433201 | C2 | semidirect |
| 3. #21422807 | C2 | semidirect |
| 5. C59⋊#1308 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 180. C59 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435099 | 2 |
| #21433201 | 2 |
| #21422807 | 2 |
| #21422448 | 2 |
| C59⋊#1308 | 2 |
| #21421957 | 2 |
| C59×#1533 | 2 |
| #9334 | 59 |