Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11752361 | C2 | semidirect |
| 2. #11751867 | C2 | semidirect |
| 4. C3×#64871 | C2 | semidirect |
| 5. #11746515 | C2 | semidirect |
| 6. #11746489 | C2 | semidirect |
| 7. C3⋊C8×#170 | C2 | semidirect |
| 31. #64871 | D3 | semidirect |
| 50. #6652 | C8 | semidirect |
| 80. C5×D12 | C2×C8 | semidirect |
| 84. C3×D20 | C2×C8 | semidirect |
| 91. C3⋊#170 | D8 | semidirect |
| 94. C3⋊#168 | C2×C8 | semidirect |
| 182. D20 | D3×C8 | semidirect |
| 224. D12 | D5⋊C8 | semidirect |
| 267. C3×C5 | C8×D8 | semidirect |
| 314. C5 | #68148 | semidirect |
| 329. C3 | #10603935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752361 | 2 |
| #11751867 | 2 |
| #11747216 | 2 |
| C3×#64871 | 2 |
| #11746515 | 2 |
| #11746489 | 2 |
| C3⋊C8×#170 | 2 |
| #10603935 | 3 |
| #68148 | 5 |