Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
852 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 852 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×C3×D20 | C2 | semidirect |
| 2. C22×#1202 | C2 | semidirect |
| 3. C22×#1202 | C2 | semidirect |
| 4. C22×D5×Dic3 | C2 | semidirect |
| 5. C2×#6714 | C2 | semidirect |
| 6. C2×C5×Dic3⋊C4 | C2 | semidirect |
| 7. C2×#6665 | C2 | semidirect |
| 8. #91409 | C2 | direct (N × H) |
| 18. C2×C3×D20 | C22 | semidirect |
| 21. C2×#1202 | C22 | semidirect |
| 22. C2×#1202 | C22 | semidirect |
| 24. C2×D5×Dic3 | C22 | semidirect |
| 25. #6714 | C22 | semidirect |
| 26. C5×Dic3⋊C4 | C22 | semidirect |
| 27. #6665 | C22 | semidirect |
| 31. C22×D20 | D3 | semidirect |
| 47. C22×C3×D5 | D4 | semidirect |
| 55. C2×C5×Dic3 | D4 | semidirect |
| 69. C2×Dic3⋊C4 | D5 | semidirect |
| 82. C2×D20 | C2×D3 | semidirect |
| 104. C2×C3×D5 | C2×D4 | semidirect |
| 108. C5×Dic3 | C2×D4 | semidirect |
| 126. Dic3⋊C4 | C2×D5 | semidirect |
| 137. C22×D5 | #67 | semidirect |
| 160. C2×C3×C5 | #121 | semidirect |
| 189. C2×Dic3 | D20 | semidirect |
| 207. C2×D5 | C2×#67 | semidirect |
| 230. C3×C5 | C2×#121 | semidirect |
| 250. Dic3 | C2×D20 | semidirect |
| 251. C2×C5 | #939 | semidirect |
| 285. C2×C3 | #4041 | semidirect |
| 290. C5 | C2×#939 | semidirect |
| 311. C3 | C2×#4041 | semidirect |
| 315. C2 | #91409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D20 | 2 |
| C22×#1202 | 2 |
| C22×D5×Dic3 | 2 |
| C2×#6714 | 2 |
| C2×C5×Dic3⋊C4 | 2 |
| C2×#6665 | 2 |
| #91409 | 2 |
| C2×#4041 | 3 |
| C2×#939 | 5 |