Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. C2×#21463315 | C2 | semidirect |
| 3. #30628257 | C2 | semidirect |
| 4. C22⋊(C491⋊C8) | C2 | semidirect |
| 5. C22⋊Q8×C491 | C2 | semidirect |
| 11. C2×C491⋊C8 | C22 | semidirect |
| 12. C2×Q8×C491 | C22 | semidirect |
| 15. C4⋊C4×C491 | C22 | semidirect |
| 34. C22×C491 | SD16 | semidirect |
| 49. C491 | #450 | semidirect |
| 53. C22⋊Q8 | D491 | semidirect |
| 57. C2×Q8 | C2×D491 | semidirect |
| 65. C4⋊C4 | C2×D491 | semidirect |
| 88. C22 | #21463315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1964 | 2 |
| C2×#21463315 | 2 |
| #30628257 | 2 |
| C22⋊(C491⋊C8) | 2 |
| C22⋊Q8×C491 | 2 |
| #450 | 491 |