Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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. Q16×Dic15 | C2 | semidirect |
| 4. C3×C5×#358 | C2 | semidirect |
| 6. C16×Dic15 | C2 | semidirect |
| 7. #11746311 | C2 | semidirect |
| 16. #91112 | C4 | semidirect |
| 25. C5×#358 | D3 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 49. C3×#358 | D5 | semidirect |
| 97. C5×Q16 | C4×D3 | semidirect |
| 114. #358 | D15 | semidirect |
| 127. Dic15 | SD32 | semidirect |
| 132. C3×Q16 | C4×D5 | semidirect |
| 206. Q16 | C4×D15 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 254. C5 | #69206 | semidirect |
| 266. C3 | #10599999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic15 | 2 |
| C2×#91112 | 2 |
| #11750973 | 2 |
| C3×C5×#358 | 2 |
| #11746330 | 2 |
| C16×Dic15 | 2 |
| #11746311 | 2 |
| #10599999 | 3 |
| #69206 | 5 |