Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#65127 | C2 | semidirect |
| 3. D12×#168 | C2 | semidirect |
| 4. #11746301 | C2 | semidirect |
| 5. C5×#4483 | C2 | semidirect |
| 6. #11745835 | C2 | semidirect |
| 7. #11745832 | C2 | semidirect |
| 27. #65127 | D3 | semidirect |
| 55. #4483 | D5 | semidirect |
| 81. C5×D12 | M16 | semidirect |
| 224. D12 | #676 | semidirect |
| 267. C3×C5 | #1586 | semidirect |
| 314. C5 | #70863 | semidirect |
| 329. C3 | #10598950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65127 | 2 |
| C4×#6652 | 2 |
| D12×#168 | 2 |
| #11746301 | 2 |
| C5×#4483 | 2 |
| #11745835 | 2 |
| #11745832 | 2 |
| #10598950 | 3 |
| #70863 | 5 |