Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11746753 | C2 | semidirect |
| 5. #11746752 | C2 | semidirect |
| 71. C3×C5×C8 | M16 | semidirect |
| 143. C5×C8 | #208 | semidirect |
| 173. C3×C8 | #700 | semidirect |
| 202. C3×C5 | #1569 | semidirect |
| 233. C8 | #6758 | semidirect |
| 238. C5 | #69851 | semidirect |
| 250. C3 | #10603866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752342 | 2 |
| #11752340 | 2 |
| C3×#64996 | 2 |
| #11746753 | 2 |
| #11746752 | 2 |
| #10603866 | 3 |
| #69851 | 5 |