Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
272 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 9. C4⋊#14523339 | C4 | semidirect |
| 11. C4×#14523339 | C4 | semidirect |
| 36. #14523339 | C4⋊C4 | semidirect |
| 58. C4×C257 | #97 | semidirect |
| 68. C257 | #1770 | semidirect |
| 127. C4 | #22551503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#14523339 | 2 |
| C2×#22551503 | 2 |
| C2×C4×#14523339 | 2 |
| #30656492 | 2 |
| C4×C4⋊C4×C257 | 2 |
| #1770 | 257 |