Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. #11746750 | C2 | semidirect |
| 4. C3×#64879 | C2 | semidirect |
| 5. #11746485 | C2 | semidirect |
| 23. #64879 | D3 | semidirect |
| 31. C8×D15 | C8 | semidirect |
| 37. #6648 | C8 | semidirect |
| 65. C3×C5×C8 | C2×C8 | semidirect |
| 66. C3⋊#168 | C2×C8 | semidirect |
| 67. C3×#168 | C2×C8 | semidirect |
| 68. C5×C3⋊C8 | C2×C8 | semidirect |
| 132. C5×C8 | D3×C8 | semidirect |
| 134. #168 | D3×C8 | semidirect |
| 148. D15 | #322 | semidirect |
| 159. C3×C8 | D5⋊C8 | semidirect |
| 162. C3⋊C8 | D5⋊C8 | semidirect |
| 185. C3×C5 | C2×#322 | semidirect |
| 210. C8 | #6738 | semidirect |
| 214. C5 | D3×#322 | semidirect |
| 223. C3 | #10603807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6738 | 2 |
| C8×#1200 | 2 |
| #11746750 | 2 |
| C3×#64879 | 2 |
| #11746485 | 2 |
| #10603807 | 3 |
| D3×#322 | 5 |