Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 84. C3×C5×Q8 | Q16 | semidirect |
| 97. Dic30 | Q16 | semidirect |
| 185. C5×Q8 | #216 | semidirect |
| 224. C3×Q8 | #689 | semidirect |
| 276. C3×C5 | #1633 | semidirect |
| 298. Q8 | #6718 | semidirect |
| 314. C5 | #71161 | semidirect |
| 327. C3 | #10601954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic30 | 2 |
| C3×C5×#477 | 2 |
| #11751193 | 2 |
| #11751192 | 2 |
| #11746356 | 2 |
| #11746305 | 2 |
| #11746302 | 2 |
| #10601954 | 3 |
| #71161 | 5 |