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. #11751914 | C2 | semidirect |
| 2. #11751913 | C2 | semidirect |
| 4. #11746755 | C2 | semidirect |
| 5. C3×C8×#170 | C2 | semidirect |
| 6. #11746491 | C2 | semidirect |
| 7. #11746489 | C2 | semidirect |
| 30. C8×#170 | D3 | semidirect |
| 93. C3×#170 | D8 | semidirect |
| 95. C3×#168 | M16 | semidirect |
| 189. #170 | D24 | semidirect |
| 191. #168 | ΓL(1,𝔽25) | semidirect |
| 267. C3×C5 | #1589 | semidirect |
| 314. C5 | #68052 | semidirect |
| 329. C3 | #10603947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751914 | 2 |
| #11751913 | 2 |
| #11747745 | 2 |
| #11746755 | 2 |
| C3×C8×#170 | 2 |
| #11746491 | 2 |
| #11746489 | 2 |
| #10603947 | 3 |
| #68052 | 5 |