Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11750944 | C2 | semidirect |
| 2. #11747045 | C2 | semidirect |
| 3. #11747029 | C2 | semidirect |
| 4. #11747009 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 6. C3×#64700 | C2 | semidirect |
| 7. #11745854 | C2 | semidirect |
| 31. #64700 | D3 | semidirect |
| 59. #4485 | D5 | semidirect |
| 100. C3×#168 | D8 | semidirect |
| 207. #168 | D24 | semidirect |
| 292. C3×C5 | #1687 | semidirect |
| 347. C5 | #68540 | semidirect |
| 364. C3 | #10599192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750944 | 2 |
| #11747045 | 2 |
| #11747029 | 2 |
| #11747009 | 2 |
| C5×#4485 | 2 |
| C3×#64700 | 2 |
| #11745854 | 2 |
| #10599192 | 3 |
| #68540 | 5 |