Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1020 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21430210 | C2 | semidirect |
| 3. C2×#16837138 | C2 | semidirect |
| 4. #21421939 | C2 | semidirect |
| 78. C22×C4×C59 | SD16 | semidirect |
| 216. C59 | #9966 | semidirect |
| 280. C22×C4 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837553 | 2 |
| #21430210 | 2 |
| C2×#16837138 | 2 |
| #21421939 | 2 |
| C59×#1438 | 2 |
| #9966 | 59 |