Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×D1028 | C2 | semidirect |
| 3. #30656489 | C2 | semidirect |
| 4. D4⋊#14523339 | C2 | semidirect |
| 5. #30656464 | C2 | semidirect |
| 6. C8×#14523339 | C2 | semidirect |
| 7. C8×D4×C257 | C2 | semidirect |
| 25. #16861603 | C8 | direct (N × H) |
| 44. D1028 | C2×C8 | semidirect |
| 51. #14523339 | C2×C8 | semidirect |
| 54. D4×C257 | C2×C8 | semidirect |
| 63. C8×C257 | D8 | semidirect |
| 83. C257 | C8×D8 | semidirect |
| 87. C8×D4 | D257 | semidirect |
| 131. D4 | C8×D257 | semidirect |
| 147. C8 | #16861603 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16861603 | 2 |
| C8×D1028 | 2 |
| #30656489 | 2 |
| D4⋊#14523339 | 2 |
| #30656464 | 2 |
| C8×#14523339 | 2 |
| C8×D4×C257 | 2 |
| C8×D8 | 257 |