Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C5×D3×Q8 | C2 | semidirect |
| 2. C2×#6717 | C2 | semidirect |
| 4. C2×#6660 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 6. #90972 | C2 | semidirect |
| 7. (C2×D3)⋊#168 | C2 | semidirect |
| 30. #3967 | D3 | semidirect |
| 35. C3×C5×Q8 | D4 | semidirect |
| 47. C5×Dic6 | D4 | semidirect |
| 52. C2×D3×Q8 | D5 | semidirect |
| 81. C2×C5×D3 | SD16 | semidirect |
| 109. C5×Q8 | D12 | semidirect |
| 138. C3×Q8 | C22⋊D5 | semidirect |
| 152. Dic6 | C22⋊D5 | semidirect |
| 183. C3×C5 | #448 | semidirect |
| 190. C2×D3 | #688 | semidirect |
| 208. Q8 | #1203 | semidirect |
| 227. C5 | #4806 | semidirect |
| 241. C3 | #65516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C2×#6717 | 2 |
| #91460 | 2 |
| C2×#6660 | 2 |
| C3×#3967 | 2 |
| #90972 | 2 |
| (C2×D3)⋊#168 | 2 |
| #65516 | 3 |
| #4806 | 5 |