Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #30656628 | C2 | semidirect |
| 4. #30656627 | C2 | semidirect |
| 6. #30656608 | C2 | semidirect |
| 7. #30656605 | C2 | semidirect |
| 8. C4×#16861595 | C2 | semidirect |
| 9. C4×C4⋊C4×C257 | C2 | semidirect |
| 13. #22551580 | C4 | semidirect |
| 34. C2×Dic514 | C2×C4 | semidirect |
| 47. #16861595 | C2×C4 | semidirect |
| 48. #16861595 | C2×C4 | semidirect |
| 58. C42×C257 | C2×C4 | semidirect |
| 118. C257 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D257 | semidirect |
| 177. 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 |
| #30656628 | 2 |
| #30656627 | 2 |
| #30656615 | 2 |
| #30656608 | 2 |
| #30656605 | 2 |
| C4×#16861595 | 2 |
| C4×C4⋊C4×C257 | 2 |
| #2337 | 257 |