Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| 2. C2×#6717 | C2 | semidirect |
| 4. #91119 | C2 | semidirect |
| 5. #91114 | C2 | semidirect |
| 19. C22×C5×Q8 | D3 | semidirect |
| 28. C3×C5×Q8 | D4 | semidirect |
| 38. C22×C3×Q8 | D5 | semidirect |
| 57. C22×C3×C5 | SD16 | semidirect |
| 81. C5×Q8 | #67 | semidirect |
| 91. C22×Q8 | D15 | semidirect |
| 105. C3×Q8 | C22⋊D5 | semidirect |
| 117. C22×C5 | #215 | semidirect |
| 137. C3×C5 | #448 | semidirect |
| 140. C22×C3 | #688 | semidirect |
| 158. Q8 | #1220 | semidirect |
| 173. C5 | #5227 | semidirect |
| 179. C22 | #6717 | semidirect |
| 185. C3 | #65516 | semidirect |
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×#6717 | 2 |
| #91819 | 2 |
| #91119 | 2 |
| #91114 | 2 |
| #65516 | 3 |
| #5227 | 5 |