Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#22547800 | C2 | semidirect |
| 2. C2×#22547799 | C2 | semidirect |
| 3. C2×#22547796 | C2 | semidirect |
| 4. #30630347 | C2 | semidirect |
| 5. #30630338 | C2 | semidirect |
| 6. #30630261 | C2 | semidirect |
| 7. C2×D8×C499 | C2 | semidirect |
| 29. C499⋊C8 | D4 | semidirect |
| 37. C8×C499 | D4 | semidirect |
| 54. C499 | #496 | semidirect |
| 59. C2×D8 | D499 | semidirect |
| 92. C8 | C22⋊D499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22547800 | 2 |
| C2×#22547799 | 2 |
| C2×#22547796 | 2 |
| #30630347 | 2 |
| #30630338 | 2 |
| #30630261 | 2 |
| C2×D8×C499 | 2 |
| #496 | 499 |