Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11754011 | C2 | semidirect |
| 2. C2×C3×#3932 | C2 | semidirect |
| 3. #11748088 | C2 | semidirect |
| 4. #11747539 | C2 | semidirect |
| 5. #11746329 | C2 | semidirect |
| 6. C5×#4510 | C2 | semidirect |
| 7. #11745921 | C2 | semidirect |
| 29. C2×#3932 | D3 | semidirect |
| 66. #4510 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #71489 | semidirect |
| 357. C3 | #10600036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754011 | 2 |
| C2×C3×#3932 | 2 |
| #11748088 | 2 |
| #11747539 | 2 |
| #11746329 | 2 |
| C5×#4510 | 2 |
| #11745921 | 2 |
| #10600036 | 3 |
| #71489 | 5 |