Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
| 3. C2×#6718 | C2 | semidirect |
| 4. #91831 | C2 | direct (N × H) |
| 5. C2×#6717 | C2 | semidirect |
| 6. C2×#6710 | C2 | semidirect |
| 11. C2×C3×C5×Q8 | C22 | semidirect |
| 20. #6718 | C22 | semidirect |
| 21. #6717 | C22 | semidirect |
| 22. #6710 | C22 | semidirect |
| 25. C22×C5×Q8 | D3 | semidirect |
| 50. C22×C3×Q8 | D5 | semidirect |
| 59. C2×C5×Q8 | C2×D3 | semidirect |
| 86. C2×C3×Q8 | C2×D5 | semidirect |
| 119. C22×Q8 | D15 | semidirect |
| 125. C2×C3×C5 | #137 | semidirect |
| 163. C2×Q8 | C2×D15 | semidirect |
| 173. C3×C5 | C2×#137 | semidirect |
| 185. C2×C5 | #942 | semidirect |
| 208. C2×C3 | #4088 | semidirect |
| 211. C5 | C2×#942 | semidirect |
| 222. C3 | C2×#4088 | semidirect |
| 225. C2 | #91831 | direct (N × H) |
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×#6817 | 2 |
| C2×#6718 | 2 |
| #91831 | 2 |
| C2×#6717 | 2 |
| C2×#6710 | 2 |
| C2×#4088 | 3 |
| C2×#942 | 5 |