Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 90 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. D4×C3⋊#170 | C2 | semidirect |
| 2. #11751928 | C2 | semidirect |
| 4. C3×D4⋊#170 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 6. #11746491 | C2 | semidirect |
| 7. #11746487 | C2 | semidirect |
| 28. D4⋊#170 | D3 | semidirect |
| 77. C3×C5×D4 | M16 | semidirect |
| 91. C3⋊#170 | D8 | semidirect |
| 173. C5×D4 | ΓL(1,𝔽25) | semidirect |
| 215. C3×D4 | #700 | semidirect |
| 267. C3×C5 | #1581 | semidirect |
| 292. D4 | #6740 | semidirect |
| 314. C5 | #68152 | semidirect |
| 329. C3 | #10603939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊#170 | 2 |
| #11751928 | 2 |
| #11748975 | 2 |
| C3×D4⋊#170 | 2 |
| #11746514 | 2 |
| #11746491 | 2 |
| #11746487 | 2 |
| #10603939 | 3 |
| #68152 | 5 |