Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#21463318 | C2 | semidirect |
| 5. #30628268 | C2 | semidirect |
| 6. #30628262 | C2 | semidirect |
| 7. #103×C491 | C2 | semidirect |
| 51. C491 | #470 | semidirect |
| 59. #103 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21463318 | 2 |
| C2×#21463311 | 2 |
| #30628317 | 2 |
| #30628313 | 2 |
| #30628268 | 2 |
| #30628262 | 2 |
| #103×C491 | 2 |
| #470 | 491 |