Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. #30656617 | C2 | semidirect |
| 3. #30656616 | C2 | semidirect |
| 4. #30656615 | C2 | semidirect |
| 5. #30656614 | C2 | semidirect |
| 6. #30656613 | C2 | semidirect |
| 7. #30656613 | C2 | semidirect |
| 8. #30656604 | C2 | semidirect |
| 9. #386×C257 | C2 | semidirect |
| 15. #22551588 | C4 | semidirect |
| 35. C2×D1028 | C2×C4 | semidirect |
| 40. C2×C22⋊D257 | C2×C4 | semidirect |
| 41. C2×C22⋊D257 | C2×C4 | semidirect |
| 55. C4×Dic257 | C2×C4 | semidirect |
| 60. C2×D4×C257 | C2×C4 | semidirect |
| 147. C257 | #2380 | semidirect |
| 156. #386 | D257 | semidirect |
| 194. C2×D4 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551588 | 2 |
| #30656617 | 2 |
| #30656616 | 2 |
| #30656615 | 2 |
| #30656614 | 2 |
| #30656613 | 2 |
| #30656604 | 2 |
| #386×C257 | 2 |
| #2380 | 257 |