Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
| 2. C2×#91113 | C2 | semidirect |
| 5. #11746313 | C2 | semidirect |
| 7. C4⋊(C3⋊#672) | C2 | semidirect |
| 23. C4×C5×Q16 | D3 | semidirect |
| 50. C3×C4×Q16 | D5 | semidirect |
| 123. C4×Q16 | D15 | semidirect |
| 238. C3×C5 | #2211 | semidirect |
| 274. C5 | #70915 | semidirect |
| 286. C3 | #10601708 | 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×#91113 | 2 |
| C2×#91112 | 2 |
| #11750797 | 2 |
| #11746313 | 2 |
| #11746312 | 2 |
| C4⋊(C3⋊#672) | 2 |
| #10601708 | 3 |
| #70915 | 5 |