Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30656868 | C2 | semidirect |
| 3. #30656490 | C2 | semidirect |
| 4. Q8⋊#14523339 | C2 | semidirect |
| 6. #30656458 | C2 | semidirect |
| 60. C8×C257 | M16 | semidirect |
| 77. C257 | #1592 | semidirect |
| 138. C8 | #16861602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656868 | 2 |
| #30656815 | 2 |
| #30656490 | 2 |
| Q8⋊#14523339 | 2 |
| D4⋊#14523339 | 2 |
| #30656458 | 2 |
| C4×SD16×C257 | 2 |
| #1592 | 257 |