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×#364 | C2 | semidirect |
| 4. #11746332 | C2 | semidirect |
| 5. #11746284 | C2 | semidirect |
| 21. C5×#364 | D3 | semidirect |
| 43. C3×#364 | D5 | semidirect |
| 106. #364 | D15 | direct (N × H) |
| 164. D15 | #364 | direct (N × H) |
| 208. C3×C5 | C2×#364 | semidirect |
| 243. C5 | D3×#364 | semidirect |
| 254. C3 | D5×#364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D15×M32 | 2 |
| C4×C8×D15 | 2 |
| C3×C5×#364 | 2 |
| #11746332 | 2 |
| #11746284 | 2 |
| D5×#364 | 3 |
| D3×#364 | 5 |