Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 108 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×#91165 | C2 | semidirect |
| 3. C4×C3⋊#674 | C2 | semidirect |
| 4. C3×C4⋊#674 | C2 | semidirect |
| 5. (C2×D3)⋊#674 | C2 | semidirect |
| 20. C4⋊#674 | D3 | semidirect |
| 33. C3⋊#674 | D4 | semidirect |
| 94. C3×C4×C5 | M32 | semidirect |
| 154. C4×C5 | #798 | semidirect |
| 170. C3×C5 | #2169 | semidirect |
| 176. C3×C4 | #3998 | semidirect |
| 200. C5 | #69279 | semidirect |
| 207. C4 | #91165 | semidirect |
| 210. C3 | #10604414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91165 | 2 |
| D12×#168 | 2 |
| C4×C3⋊#674 | 2 |
| C3×C4⋊#674 | 2 |
| (C2×D3)⋊#674 | 2 |
| #10604414 | 3 |
| #69279 | 5 |