Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11751928 | C2 | semidirect |
| 3. C8×C3⋊#170 | C2 | semidirect |
| 4. C3×#64882 | C2 | semidirect |
| 5. #11746490 | C2 | semidirect |
| 20. #64882 | D3 | semidirect |
| 63. C3⋊#170 | D8 | semidirect |
| 65. C3×C5×C8 | M16 | semidirect |
| 131. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 158. C3×C8 | #700 | semidirect |
| 185. C3×C5 | #1589 | semidirect |
| 214. C8 | #6740 | semidirect |
| 219. C5 | #68563 | semidirect |
| 230. C3 | #10604067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751928 | 2 |
| #11747766 | 2 |
| C8×C3⋊#170 | 2 |
| C3×#64882 | 2 |
| #11746490 | 2 |
| #10604067 | 3 |
| #68563 | 5 |