Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11751177 | C2 | semidirect |
| 3. D4×C3⋊#168 | C2 | semidirect |
| 4. #11751108 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11746307 | C2 | semidirect |
| 7. #11746301 | C2 | semidirect |
| 83. C3×C5×D4 | SD16 | semidirect |
| 97. C3⋊#168 | D8 | semidirect |
| 182. C5×D4 | #214 | semidirect |
| 225. C3×D4 | #687 | semidirect |
| 274. C3×C5 | #1665 | semidirect |
| 304. D4 | #6716 | semidirect |
| 322. C5 | #71004 | semidirect |
| 337. C3 | #10601797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#459 | 2 |
| #11751177 | 2 |
| D4×C3⋊#168 | 2 |
| #11751108 | 2 |
| #11746365 | 2 |
| #11746307 | 2 |
| #11746301 | 2 |
| #10601797 | 3 |
| #71004 | 5 |