Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 124 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. #11750783 | C2 | semidirect |
| 3. #11747066 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. C3×C8×#168 | C2 | semidirect |
| 21. C8×#168 | D3 | semidirect |
| 58. C3×C5×C8 | SD16 | semidirect |
| 60. C3×#168 | D8 | semidirect |
| 116. C5×C8 | #204 | semidirect |
| 118. #168 | D24 | semidirect |
| 143. C3×C8 | #687 | semidirect |
| 164. C3×C5 | #1706 | semidirect |
| 188. C8 | #6659 | semidirect |
| 193. C5 | #68058 | semidirect |
| 202. C3 | #10602067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750783 | 2 |
| C5×#4695 | 2 |
| #11747066 | 2 |
| #11746906 | 2 |
| C3×C8×#168 | 2 |
| #10602067 | 3 |
| #68058 | 5 |