Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #11747793 | C2 | semidirect |
| 3. C5×Dic3×C16 | C2 | semidirect |
| 4. C3×#64724 | C2 | semidirect |
| 5. #11745895 | C2 | semidirect |
| 10. D240 | C4 | semidirect |
| 20. #64724 | D3 | semidirect |
| 25. D120 | C2×C4 | semidirect |
| 30. C3×C5×C16 | C2×C4 | semidirect |
| 35. Dic3×C16 | D5 | semidirect |
| 75. C5×C16 | C4×D3 | semidirect |
| 89. C5×Dic3 | D16 | semidirect |
| 99. C3×C16 | C4×D5 | semidirect |
| 154. C16 | #1200 | semidirect |
| 155. C3×C5 | C4×D16 | semidirect |
| 164. Dic3 | D80 | semidirect |
| 184. C5 | #69317 | semidirect |
| 194. C3 | C4×D80 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D240 | 2 |
| #11747793 | 2 |
| C5×Dic3×C16 | 2 |
| C3×#64724 | 2 |
| #11745895 | 2 |
| C4×D80 | 3 |
| #69317 | 5 |