Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
372 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 372 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×#6762 | C2 | semidirect |
| 3. C2×C3×#704 | C2 | semidirect |
| 4. #91174 | C2 | direct (N × H) |
| 16. #6762 | C22 | semidirect |
| 19. C3×#704 | C22 | semidirect |
| 24. C2×#704 | D3 | semidirect |
| 63. #704 | C2×D3 | semidirect |
| 125. C2×C3×C5 | #100 | semidirect |
| 181. C3×C5 | C2×#100 | semidirect |
| 201. C2×C5 | #823 | semidirect |
| 227. C2×C3 | #4013 | semidirect |
| 231. C5 | C2×#823 | semidirect |
| 248. C3 | C2×#4013 | semidirect |
| 253. C2 | #91174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1203 | 2 |
| C2×#6762 | 2 |
| C2×C3×#704 | 2 |
| #91174 | 2 |
| C2×#4013 | 3 |
| C2×#823 | 5 |