Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
182 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 69 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. #30656816 | C2 | semidirect |
| 3. #30656489 | C2 | semidirect |
| 4. D4⋊#14523339 | C2 | semidirect |
| 5. #30656464 | C2 | semidirect |
| 6. #30656458 | C2 | semidirect |
| 7. C8×D4×C257 | C2 | semidirect |
| 54. D4×C257 | M16 | semidirect |
| 63. C8×C257 | D8 | semidirect |
| 83. C257 | #1581 | semidirect |
| 87. C8×D4 | D257 | semidirect |
| 131. D4 | #16861601 | semidirect |
| 147. C8 | #16861603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16861603 | 2 |
| #30656816 | 2 |
| #30656489 | 2 |
| D4⋊#14523339 | 2 |
| #30656464 | 2 |
| #30656458 | 2 |
| C8×D4×C257 | 2 |
| #1581 | 257 |