Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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×#22551525 | C2 | semidirect |
| 3. C2×#22551513 | C2 | semidirect |
| 4. C2×#22551512 | C2 | semidirect |
| 5. C2×C4×#14523339 | C2 | semidirect |
| 6. #30656639 | C2 | semidirect |
| 7. #390×C257 | C2 | semidirect |
| 11. C2×#16861603 | C4 | semidirect |
| 69. #14523339 | C22⋊C4 | semidirect |
| 84. C2×C4×C257 | D8 | semidirect |
| 120. C257 | #1970 | semidirect |
| 128. #390 | D257 | semidirect |
| 203. C2×C4 | #16861603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16861603 | 2 |
| C2×#22551525 | 2 |
| C2×#22551513 | 2 |
| C2×#22551512 | 2 |
| C2×C4×#14523339 | 2 |
| #30656639 | 2 |
| #390×C257 | 2 |
| #1970 | 257 |