Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 102 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. Dic6×#168 | C2 | semidirect |
| 4. #11746301 | C2 | semidirect |
| 5. C5×#4484 | C2 | semidirect |
| 7. #11745831 | C2 | semidirect |
| 54. #4484 | D5 | semidirect |
| 80. C5×Dic6 | M16 | semidirect |
| 91. C3×#168 | SD16 | semidirect |
| 182. #168 | #214 | semidirect |
| 214. Dic6 | #676 | semidirect |
| 252. C3×C5 | #1583 | semidirect |
| 293. C5 | #70864 | semidirect |
| 306. C3 | #10599010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65127 | 2 |
| C4×#6655 | 2 |
| Dic6×#168 | 2 |
| #11746301 | 2 |
| C5×#4484 | 2 |
| #11745835 | 2 |
| #11745831 | 2 |
| #10599010 | 3 |
| #70864 | 5 |