Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 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 |
|---|---|---|
| 1. #21422887 | C2 | semidirect |
| 2. #21422885 | C2 | semidirect |
| 3. #21422884 | C2 | semidirect |
| 6. C59⋊#1309 | C2 | semidirect |
| 172. C59 | #10611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422887 | 2 |
| #21422885 | 2 |
| #21422884 | 2 |
| #21422764 | 2 |
| C59⋊#1309 | 2 |
| C59×#1545 | 2 |
| #10611 | 59 |