Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 3. C2×#16837342 | C2 | semidirect |
| 4. #21424187 | C2 | semidirect |
| 5. C2×#16837127 | C2 | semidirect |
| 6. #21421975 | C2 | semidirect |
| 270. C59 | #9921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837718 | 2 |
| #21429840 | 2 |
| C2×#16837342 | 2 |
| #21424187 | 2 |
| C2×#16837127 | 2 |
| #21421975 | 2 |
| C2×C59×#327 | 2 |
| #9921 | 59 |