Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 174 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×Q8×D15 | C2 | semidirect |
| 2. C2×C3×Q8×D5 | C2 | semidirect |
| 3. C5×Q8×Dic3 | C2 | semidirect |
| 5. #91390 | C2 | semidirect |
| 6. #91389 | C2 | semidirect |
| 7. #91360 | C2 | semidirect |
| 25. C2×Q8×D5 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 43. #1202 | Q8 | direct (N × H) |
| 47. Q8×Dic3 | D5 | semidirect |
| 69. C2×D15 | C2×Q8 | semidirect |
| 72. C2×C3×D5 | C2×Q8 | semidirect |
| 77. C5×Dic3 | C2×Q8 | semidirect |
| 94. C5×Q8 | #67 | semidirect |
| 120. C3×Q8 | D20 | semidirect |
| 136. C2×D5 | D3×Q8 | semidirect |
| 156. C3×C5 | D4×Q8 | semidirect |
| 168. Dic3 | Q8×D5 | semidirect |
| 178. Q8 | #1202 | direct (N × H) |
| 192. C5 | Q8×#67 | semidirect |
| 205. C3 | Q8×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D15 | 2 |
| C2×C3×Q8×D5 | 2 |
| C5×Q8×Dic3 | 2 |
| C4×#1202 | 2 |
| #91390 | 2 |
| #91389 | 2 |
| #91360 | 2 |
| Q8×D20 | 3 |
| Q8×#67 | 5 |