Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 364 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. #11750935 | C2 | semidirect |
| 3. #11747014 | C2 | semidirect |
| 4. C5×#4483 | C2 | semidirect |
| 5. C3×#64699 | C2 | semidirect |
| 6. #11745838 | C2 | semidirect |
| 7. #11745833 | C2 | semidirect |
| 29. #64699 | D3 | semidirect |
| 56. #4483 | D5 | semidirect |
| 81. D60 | M16 | semidirect |
| 91. C3⋊#168 | D8 | semidirect |
| 267. C3×C5 | #1581 | semidirect |
| 314. C5 | #68559 | semidirect |
| 329. C3 | #10598946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750935 | 2 |
| C4×#6654 | 2 |
| #11747014 | 2 |
| C5×#4483 | 2 |
| C3×#64699 | 2 |
| #11745838 | 2 |
| #11745833 | 2 |
| #10598946 | 3 |
| #68559 | 5 |