Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C22×#16861606 | C2 | semidirect |
| 2. C2×#22551571 | C2 | semidirect |
| 3. C2×#22551515 | C2 | semidirect |
| 4. C2×#22551513 | C2 | semidirect |
| 5. C2×C22⋊#14523339 | C2 | semidirect |
| 6. #30656499 | C2 | semidirect |
| 34. C2×Dic514 | D4 | semidirect |
| 43. C2×#14523339 | D4 | semidirect |
| 45. C4⋊Dic257 | D4 | semidirect |
| 96. C23×C257 | SD16 | semidirect |
| 157. C257 | #2000 | semidirect |
| 242. C23 | #16861606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861606 | 2 |
| C2×#22551571 | 2 |
| C2×#22551515 | 2 |
| C2×#22551513 | 2 |
| C2×C22⋊#14523339 | 2 |
| #30656499 | 2 |
| C2×#121×C257 | 2 |
| #2000 | 257 |