Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 1. C5×#4693 | C2 | semidirect |
| 2. C3×#64982 | C2 | semidirect |
| 4. #11746962 | C2 | semidirect |
| 5. #11746901 | C2 | semidirect |
| 6. #11746895 | C2 | semidirect |
| 7. C8×C3⋊#168 | C2 | semidirect |
| 28. #64982 | D3 | semidirect |
| 54. #4693 | D5 | semidirect |
| 85. C3×C5×C8 | D8 | semidirect |
| 87. C3⋊#168 | SD16 | semidirect |
| 173. C5×C8 | #213 | semidirect |
| 209. C3×C8 | #686 | semidirect |
| 243. C3×C5 | #1706 | semidirect |
| 278. C8 | #6652 | semidirect |
| 284. C5 | #71255 | semidirect |
| 297. C3 | #10602048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4693 | 2 |
| C3×#64982 | 2 |
| #11747039 | 2 |
| #11746962 | 2 |
| #11746901 | 2 |
| #11746895 | 2 |
| C8×C3⋊#168 | 2 |
| #10602048 | 3 |
| #71255 | 5 |