Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
380 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C2×#6740 | C2 | semidirect |
| 3. #91241 | C2 | semidirect |
| 4. C3×C22⋊#170 | C2 | semidirect |
| 5. #91171 | C2 | semidirect |
| 15. C2×C3⋊#170 | C22 | semidirect |
| 16. C2×C3×#170 | C22 | semidirect |
| 22. C22⋊#170 | D3 | semidirect |
| 56. C2×#170 | C2×D3 | semidirect |
| 61. C22×C3×C5 | M16 | semidirect |
| 69. C2×D15 | M16 | semidirect |
| 134. C22×C5 | ΓL(1,𝔽25) | semidirect |
| 158. C3×C5 | #407 | semidirect |
| 161. C22×C3 | #700 | semidirect |
| 204. C5 | #4726 | semidirect |
| 214. C22 | #6740 | semidirect |
| 220. C3 | #65756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1200 | 2 |
| C2×#6740 | 2 |
| #91241 | 2 |
| C3×C22⋊#170 | 2 |
| #91171 | 2 |
| #65756 | 3 |
| #4726 | 5 |