Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
560 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 114 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. #11751174 | C2 | semidirect |
| 2. C5×#5073 | C2 | semidirect |
| 3. C3×#65362 | C2 | semidirect |
| 4. #11747039 | C2 | semidirect |
| 5. #11747035 | C2 | semidirect |
| 6. #11747029 | C2 | semidirect |
| 7. C3⋊C8×#168 | C2 | semidirect |
| 27. #65362 | D3 | semidirect |
| 56. #5073 | D5 | semidirect |
| 92. C3⋊#168 | D8 | semidirect |
| 93. C3×#168 | D8 | semidirect |
| 94. C5×C3⋊C8 | D8 | semidirect |
| 196. #168 | #213 | semidirect |
| 238. C3⋊C8 | #686 | semidirect |
| 277. C3×C5 | #1712 | semidirect |
| 330. C5 | #71276 | semidirect |
| 347. C3 | #10602069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751174 | 2 |
| C5×#5073 | 2 |
| C3×#65362 | 2 |
| #11747039 | 2 |
| #11747035 | 2 |
| #11747029 | 2 |
| C3⋊C8×#168 | 2 |
| #10602069 | 3 |
| #71276 | 5 |