Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#22551527 | C2 | semidirect |
| 3. C2×#22551520 | C2 | semidirect |
| 4. #30656705 | C2 | semidirect |
| 5. #30656704 | C2 | semidirect |
| 6. C2×C4×#14523339 | C2 | semidirect |
| 7. C2×#104×C257 | C2 | semidirect |
| 11. C2×#16861608 | C4 | semidirect |
| 12. C2×#16861606 | C4 | semidirect |
| 13. C2×#16861605 | C4 | semidirect |
| 14. C2×#16861603 | C4 | semidirect |
| 119. C257 | #1974 | semidirect |
| 124. C2×#104 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551612 | 2 |
| C2×#22551527 | 2 |
| C2×#22551520 | 2 |
| #30656705 | 2 |
| #30656704 | 2 |
| C2×C4×#14523339 | 2 |
| C2×#104×C257 | 2 |
| #1974 | 257 |