Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 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. #30656641 | C2 | semidirect |
| 3. #30656629 | C2 | semidirect |
| 4. #30656627 | C2 | semidirect |
| 6. #30656611 | C2 | semidirect |
| 7. #30656608 | C2 | semidirect |
| 8. #30656603 | C2 | semidirect |
| 9. #382×C257 | C2 | semidirect |
| 13. #22551580 | C4 | semidirect |
| 35. C2×Dic514 | C2×C4 | semidirect |
| 51. #16861595 | C2×C4 | semidirect |
| 52. #16861595 | C2×C4 | semidirect |
| 61. C42×C257 | C2×C4 | semidirect |
| 127. C257 | #2379 | semidirect |
| 137. #382 | D257 | semidirect |
| 189. C42 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551580 | 2 |
| #30656641 | 2 |
| #30656629 | 2 |
| #30656627 | 2 |
| #30656615 | 2 |
| #30656611 | 2 |
| #30656608 | 2 |
| #30656603 | 2 |
| #382×C257 | 2 |
| #2379 | 257 |