Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 3. #11746276 | C2 | semidirect |
| 4. C3×C8×#168 | C2 | semidirect |
| 5. #11745831 | C2 | semidirect |
| 21. C8×#168 | D3 | semidirect |
| 55. C3×C5×C8 | M16 | semidirect |
| 57. C3×#168 | M16 | semidirect |
| 110. C5×C8 | ΓL(1,𝔽25) | semidirect |
| 112. #168 | ΓL(1,𝔽25) | semidirect |
| 133. C3×C8 | #681 | semidirect |
| 154. C3×C5 | #1455 | semidirect |
| 175. C8 | #6650 | semidirect |
| 179. C5 | #68050 | semidirect |
| 187. C3 | #10600642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×ΓL(1,𝔽25) | 2 |
| C4×#6650 | 2 |
| #11746276 | 2 |
| C3×C8×#168 | 2 |
| #11745831 | 2 |
| #10600642 | 3 |
| #68050 | 5 |