Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
644 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 192 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×#1204 | C2 | semidirect |
| 3. C2×C4⋊Dic15 | C2 | semidirect |
| 4. C2×C5×Dic3⋊C4 | C2 | semidirect |
| 6. C2×Dic3⋊Dic5 | C2 | semidirect |
| 8. #91422 | C2 | direct (N × H) |
| 18. C2×#1204 | C22 | semidirect |
| 21. C4⋊Dic15 | C22 | semidirect |
| 22. C5×Dic3⋊C4 | C22 | semidirect |
| 24. Dic3⋊Dic5 | C22 | semidirect |
| 38. C22×C3×D5 | Q8 | semidirect |
| 60. C2×Dic3⋊C4 | D5 | semidirect |
| 86. C2×C3×D5 | C2×Q8 | semidirect |
| 108. Dic3⋊C4 | C2×D5 | semidirect |
| 112. C22×D5 | Dic6 | semidirect |
| 136. C2×C3×C5 | C22⋊Q8 | semidirect |
| 167. C2×D5 | C2×Dic6 | semidirect |
| 190. C3×C5 | C2×C22⋊Q8 | semidirect |
| 205. C2×C5 | #878 | semidirect |
| 230. C2×C3 | #4043 | semidirect |
| 234. C5 | C2×#878 | semidirect |
| 249. C3 | C2×#4043 | semidirect |
| 251. C2 | #91422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1204 | 2 |
| C22×D5×Dic3 | 2 |
| C2×C4⋊Dic15 | 2 |
| C2×C5×Dic3⋊C4 | 2 |
| C2×C3×#685 | 2 |
| C2×Dic3⋊Dic5 | 2 |
| C2×#6665 | 2 |
| #91422 | 2 |
| C2×#4043 | 3 |
| C2×#878 | 5 |