Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. C2×#14273673 | C4 | semidirect |
| 180. C59 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273673 | 2 |
| #21432964 | 2 |
| #21425817 | 2 |
| #21425009 | 2 |
| #21422193 | 2 |
| #21422186 | 2 |
| C2×C59×#362 | 2 |
| #13020 | 59 |