Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×C3×C5×SD32 | C2 | semidirect |
| 2. Q16×Dic15 | C2 | semidirect |
| 3. C2×#91112 | C2 | semidirect |
| 5. #11746383 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746322 | C2 | semidirect |
| 23. C2×C5×SD32 | D3 | semidirect |
| 36. C3×C5×Q16 | D4 | semidirect |
| 50. C2×C3×SD32 | D5 | semidirect |
| 108. C5×Q16 | #67 | semidirect |
| 123. C2×SD32 | D15 | semidirect |
| 141. Dic15 | SD32 | semidirect |
| 148. C3×Q16 | C22⋊D5 | semidirect |
| 235. Q16 | #1220 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 291. C5 | #71475 | semidirect |
| 305. C3 | #10602268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD32 | 2 |
| Q16×Dic15 | 2 |
| C2×#91112 | 2 |
| #11751252 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| #11746322 | 2 |
| #10602268 | 3 |
| #71475 | 5 |