Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16837735 | C2 | semidirect |
| 3. #21425082 | C2 | semidirect |
| 4. #21424187 | C2 | semidirect |
| 6. #21421943 | C2 | semidirect |
| 240. C59 | #9958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837735 | 2 |
| #21428589 | 2 |
| #21425082 | 2 |
| #21424187 | 2 |
| #21422664 | 2 |
| #21421943 | 2 |
| C59×#3187 | 2 |
| #9958 | 59 |