Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11750795 | C2 | semidirect |
| 2. C5×#4693 | C2 | semidirect |
| 3. #11747066 | C2 | semidirect |
| 5. #11746941 | C2 | semidirect |
| 6. #11746912 | C2 | semidirect |
| 7. C3×#64674 | C2 | semidirect |
| 29. #64674 | D3 | semidirect |
| 53. #4693 | D5 | semidirect |
| 87. C3×#168 | SD16 | semidirect |
| 175. #168 | #204 | semidirect |
| 243. C3×C5 | #1715 | semidirect |
| 284. C5 | #68091 | semidirect |
| 297. C3 | #10602052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750795 | 2 |
| C5×#4693 | 2 |
| #11747066 | 2 |
| #11747029 | 2 |
| #11746941 | 2 |
| #11746912 | 2 |
| C3×#64674 | 2 |
| #10602052 | 3 |
| #68091 | 5 |