Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #11751113 | C2 | semidirect |
| 3. #11750935 | C2 | semidirect |
| 4. C3×C5×D4⋊C8 | C2 | semidirect |
| 5. #11746301 | C2 | semidirect |
| 6. #11746280 | C2 | semidirect |
| 7. #11746276 | C2 | semidirect |
| 28. C5×D4⋊C8 | D3 | semidirect |
| 54. C3×D4⋊C8 | D5 | semidirect |
| 86. D60 | M16 | semidirect |
| 135. D4⋊C8 | D15 | semidirect |
| 267. C3×C5 | #1586 | semidirect |
| 314. C5 | #68158 | semidirect |
| 329. C3 | #10598951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6715 | 2 |
| #11751113 | 2 |
| #11750935 | 2 |
| C3×C5×D4⋊C8 | 2 |
| #11746301 | 2 |
| #11746280 | 2 |
| #11746276 | 2 |
| #10598951 | 3 |
| #68158 | 5 |