Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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. Dic6×#170 | C2 | semidirect |
| 5. #11746515 | C2 | semidirect |
| 6. #11746492 | C2 | semidirect |
| 7. #11746487 | C2 | semidirect |
| 80. C5×Dic6 | M16 | semidirect |
| 214. Dic6 | #704 | semidirect |
| 252. C3×C5 | #1588 | semidirect |
| 293. C5 | #70865 | semidirect |
| 306. C3 | #10604812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65774 | 2 |
| Dic6×#170 | 2 |
| Dic5×#214 | 2 |
| D4⋊(C3⋊#170) | 2 |
| #11746515 | 2 |
| #11746492 | 2 |
| #11746487 | 2 |
| #10604812 | 3 |
| #70865 | 5 |