Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 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. #11751193 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11746307 | C2 | semidirect |
| 7. #11746300 | C2 | semidirect |
| 78. C3×C5×D4 | Q16 | semidirect |
| 170. C5×D4 | #216 | semidirect |
| 209. C3×D4 | #689 | semidirect |
| 256. C3×C5 | #1669 | semidirect |
| 279. D4 | #6718 | semidirect |
| 297. C5 | #71101 | semidirect |
| 310. C3 | #10601894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#474 | 2 |
| #11751193 | 2 |
| D4×C3⋊#168 | 2 |
| #11751108 | 2 |
| #11746368 | 2 |
| #11746307 | 2 |
| #11746300 | 2 |
| #10601894 | 3 |
| #71101 | 5 |