Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
684 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. C22×#1200 | C2 | semidirect |
| 3. C2×C5×Dic3⋊C4 | C2 | semidirect |
| 4. C2×C3×#683 | C2 | semidirect |
| 5. C2×#6667 | C2 | semidirect |
| 6. C2×#6667 | C2 | semidirect |
| 7. C2×#6667 | C2 | semidirect |
| 8. #91433 | C2 | direct (N × H) |
| 20. C2×#1200 | C22 | semidirect |
| 21. C5×Dic3⋊C4 | C22 | semidirect |
| 22. C3×#683 | C22 | semidirect |
| 23. #6667 | C22 | semidirect |
| 24. #6667 | C22 | semidirect |
| 25. #6667 | C22 | semidirect |
| 33. C2×#683 | D3 | semidirect |
| 62. C2×Dic3⋊C4 | D5 | semidirect |
| 79. #683 | C2×D3 | semidirect |
| 113. Dic3⋊C4 | C2×D5 | semidirect |
| 143. C2×C3×C5 | #123 | semidirect |
| 203. C3×C5 | C2×#123 | semidirect |
| 221. C2×C5 | #894 | semidirect |
| 248. C2×C3 | #4040 | semidirect |
| 254. C5 | C2×#894 | semidirect |
| 272. C3 | C2×#4040 | semidirect |
| 275. C2 | #91433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D60 | 2 |
| C22×#1200 | 2 |
| C2×C5×Dic3⋊C4 | 2 |
| C2×C3×#683 | 2 |
| C2×#6667 | 2 |
| #91433 | 2 |
| C2×#4040 | 3 |
| C2×#894 | 5 |