Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
| 4. #11758423 | C2 | semidirect |
| 6. #11758395 | C2 | semidirect |
| 7. #11758391 | C2 | semidirect |
| 15. #92481 | C4 | semidirect |
| 22. Q8×C31 | C2×C4 | semidirect |
| 33. C31⋊C8 | C2×C4 | semidirect |
| 51. C4×Q8 | D31 | semidirect |
| 57. C31 | #440 | semidirect |
| 72. Q8 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C31 | 2 |
| C2×#92481 | 2 |
| C4×D124 | 2 |
| #11758423 | 2 |
| #11758397 | 2 |
| #11758395 | 2 |
| #11758391 | 2 |
| #440 | 31 |