Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 66. C3×C5×C8 | Q16 | semidirect |
| 131. C5×C8 | #216 | semidirect |
| 159. C3×C8 | #689 | semidirect |
| 183. C3×C5 | #1674 | semidirect |
| 209. C8 | #6718 | semidirect |
| 213. C5 | #70944 | semidirect |
| 223. C3 | #10601737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C8×Q8 | 2 |
| #11751132 | 2 |
| #11750783 | 2 |
| #11746307 | 2 |
| #11746279 | 2 |
| #10601737 | 3 |
| #70944 | 5 |