Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. C3×C5×#367 | C2 | semidirect |
| 4. #11746326 | C2 | semidirect |
| 5. #11746311 | C2 | semidirect |
| 14. C16×D15 | C4 | semidirect |
| 18. C5×#367 | D3 | semidirect |
| 30. C3×C5×C16 | C2×C4 | semidirect |
| 31. C3⋊#672 | C2×C4 | semidirect |
| 34. C3×#367 | D5 | semidirect |
| 74. C5×C16 | C4×D3 | semidirect |
| 80. #367 | D15 | direct (N × H) |
| 98. C3×C16 | C4×D5 | semidirect |
| 121. D15 | #367 | direct (N × H) |
| 151. C16 | C4×D15 | semidirect |
| 152. C3×C5 | C2×#367 | semidirect |
| 178. C5 | D3×#367 | semidirect |
| 187. C3 | D5×#367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D15 | 2 |
| D15×#107 | 2 |
| C3×C5×#367 | 2 |
| #11746326 | 2 |
| #11746311 | 2 |
| D5×#367 | 3 |
| D3×#367 | 5 |