Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 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. C2×C3×#3990 | C2 | semidirect |
| 2. C2×#91166 | C2 | semidirect |
| 4. #11746758 | C2 | semidirect |
| 5. Dic3⋊#674 | C2 | semidirect |
| 6. #11746547 | C2 | semidirect |
| 7. Dic3×#674 | C2 | semidirect |
| 24. C2×#3990 | D3 | semidirect |
| 48. C3×#674 | D4 | semidirect |
| 118. #674 | #67 | semidirect |
| 138. C5×Dic3 | M32 | semidirect |
| 242. C3×C5 | #2169 | semidirect |
| 255. Dic3 | #3990 | semidirect |
| 283. C5 | #71430 | semidirect |
| 297. C3 | #10604023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3990 | 2 |
| C2×#91166 | 2 |
| #11747698 | 2 |
| #11746758 | 2 |
| Dic3⋊#674 | 2 |
| #11746547 | 2 |
| Dic3×#674 | 2 |
| #10604023 | 3 |
| #71430 | 5 |