Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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. C3×C4×C5×Q16 | C2 | semidirect |
| 4. #11746385 | C2 | semidirect |
| 6. #11746311 | C2 | semidirect |
| 7. C4×C3⋊#672 | C2 | semidirect |
| 16. #91112 | C4 | direct (N × H) |
| 22. C4×C5×Q16 | D3 | semidirect |
| 33. C3×C5×Q16 | C2×C4 | semidirect |
| 45. C3⋊#672 | C2×C4 | semidirect |
| 46. C3×C4×Q16 | D5 | semidirect |
| 97. C5×Q16 | C4×D3 | semidirect |
| 111. C4×Q16 | D15 | semidirect |
| 124. C3×C4×C5 | SD32 | semidirect |
| 132. C3×Q16 | C4×D5 | semidirect |
| 198. C4×C5 | #828 | semidirect |
| 206. Q16 | C4×D15 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 227. C3×C4 | #3960 | semidirect |
| 254. C5 | C4×#828 | semidirect |
| 263. C4 | #91112 | direct (N × H) |
| 266. C3 | C4×#3960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q16 | 2 |
| C2×#91112 | 2 |
| C4×D120 | 2 |
| #11746385 | 2 |
| #11746312 | 2 |
| #11746311 | 2 |
| C4×C3⋊#672 | 2 |
| C4×#3960 | 3 |
| C4×#828 | 5 |