Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×Q8×C31 | C2 | semidirect |
| 2. #11758524 | C2 | semidirect |
| 3. #11758523 | C2 | semidirect |
| 4. #11758475 | C2 | semidirect |
| 6. #11758471 | C2 | semidirect |
| 7. #11758467 | C2 | semidirect |
| 8. C4×D124 | C2 | semidirect |
| 9. C4×D124 | C2 | semidirect |
| 10. #11758449 | C2 | semidirect |
| 11. C42×D31 | C2 | semidirect |
| 81. C4×Q8 | D31 | semidirect |
| 86. C31 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C31 | 2 |
| #11758524 | 2 |
| #11758523 | 2 |
| #11758475 | 2 |
| #11758472 | 2 |
| #11758471 | 2 |
| #11758467 | 2 |
| C4×D124 | 2 |
| #11758449 | 2 |
| C42×D31 | 2 |
| #529 | 31 |