Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 4. #11746512 | C2 | semidirect |
| 66. C5×C3⋊C8 | M16 | semidirect |
| 165. C3⋊C8 | #700 | semidirect |
| 191. C3×C5 | #1566 | semidirect |
| 226. C5 | #70490 | semidirect |
| 238. C3 | #10603816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752340 | 2 |
| C3×#65681 | 2 |
| C4×D5×C3⋊C8 | 2 |
| #11746512 | 2 |
| #10603816 | 3 |
| #70490 | 5 |