Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
154 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 27 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. C5×Q8×A4 | C2 | semidirect |
| 3. A4⋊#168 | C2 | semidirect |
| 10. C22×C5×Q8 | D3 | semidirect |
| 22. Q8×A4 | D5 | semidirect |
| 41. C5×A4 | SD16 | semidirect |
| 53. C5×Q8 | S4 | semidirect |
| 65. C22×Q8 | D15 | semidirect |
| 81. C22×C5 | #215 | semidirect |
| 106. A4 | #688 | semidirect |
| 118. Q8 | C5⋊S4 | semidirect |
| 132. C5 | #5417 | semidirect |
| 138. C22 | #6717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×A4 | 2 |
| C4⋊(C5⋊S4) | 2 |
| A4⋊#168 | 2 |
| #65516 | 3 |
| #6717 | 4 |
| #5417 | 5 |