Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
408 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11750796 | C2 | semidirect |
| 2. C5×C8×D12 | C2 | semidirect |
| 3. #11747037 | C2 | semidirect |
| 4. C3×#64678 | C2 | semidirect |
| 5. #11745854 | C2 | semidirect |
| 23. #64678 | D3 | semidirect |
| 42. C8×D12 | D5 | semidirect |
| 69. C5×D12 | D8 | semidirect |
| 73. C3×C5×C8 | D8 | semidirect |
| 154. C5×C8 | D24 | semidirect |
| 184. D12 | D40 | semidirect |
| 189. C3×C8 | #686 | semidirect |
| 220. C3×C5 | #1667 | semidirect |
| 257. C8 | #6654 | semidirect |
| 263. C5 | #68576 | semidirect |
| 277. C3 | #10601640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750796 | 2 |
| C5×C8×D12 | 2 |
| #11747037 | 2 |
| C3×#64678 | 2 |
| #11745854 | 2 |
| #10601640 | 3 |
| #68576 | 5 |