Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×C3×C5×Q8 | C2 | semidirect |
| 2. C2×Q8×D15 | C2 | semidirect |
| 3. #91835 | C2 | semidirect |
| 4. Q8×Dic15 | C2 | semidirect |
| 5. #91833 | C2 | semidirect |
| 7. #91813 | C2 | semidirect |
| 24. C22×C5×Q8 | D3 | semidirect |
| 34. C3×C5×Q8 | D4 | semidirect |
| 38. #1220 | Q8 | direct (N × H) |
| 44. C22×C3×Q8 | D5 | semidirect |
| 68. C22×C3×C5 | C2×Q8 | semidirect |
| 72. C2×D15 | C2×Q8 | semidirect |
| 77. Dic15 | C2×Q8 | semidirect |
| 95. C5×Q8 | #67 | semidirect |
| 106. C22×Q8 | D15 | semidirect |
| 120. C3×Q8 | C22⋊D5 | semidirect |
| 132. C22×C5 | D3×Q8 | semidirect |
| 156. C3×C5 | D4×Q8 | semidirect |
| 159. C22×C3 | Q8×D5 | semidirect |
| 178. Q8 | #1220 | direct (N × H) |
| 192. C5 | Q8×#67 | semidirect |
| 198. C22 | Q8×D15 | semidirect |
| 205. C3 | Q8×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C2×Q8×D15 | 2 |
| #91835 | 2 |
| Q8×Dic15 | 2 |
| #91833 | 2 |
| C4×#1220 | 2 |
| #91813 | 2 |
| Q8×C22⋊D5 | 3 |
| Q8×#67 | 5 |