Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11756322 | C2 | semidirect |
| 2. C5×#5015 | C2 | semidirect |
| 3. #11747066 | C2 | semidirect |
| 4. #11747045 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745863 | C2 | semidirect |
| 7. #11745839 | C2 | semidirect |
| 31. D4⋊#168 | D3 | semidirect |
| 60. #5015 | D5 | semidirect |
| 323. C3×C5 | #1624 | semidirect |
| 381. C5 | #68199 | semidirect |
| 400. C3 | #10601810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756322 | 2 |
| C5×#5015 | 2 |
| #11747066 | 2 |
| #11747045 | 2 |
| C3×D4⋊#168 | 2 |
| #11745863 | 2 |
| #11745839 | 2 |
| #10601810 | 3 |
| #68199 | 5 |