Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 89. C3×#168 | Q16 | semidirect |
| 176. #168 | #216 | semidirect |
| 241. C3×C5 | #1694 | semidirect |
| 276. C5 | #71379 | semidirect |
| 287. C3 | #10601850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5090 | 2 |
| C3×#65367 | 2 |
| #11747099 | 2 |
| #11746863 | 2 |
| #11746368 | 2 |
| #11745864 | 2 |
| #11745856 | 2 |
| #10601850 | 3 |
| #71379 | 5 |