Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#22551535 | C2 | semidirect |
| 2. C2×#22551533 | C2 | semidirect |
| 3. #30656973 | C2 | semidirect |
| 4. #30656541 | C2 | semidirect |
| 5. #30656538 | C2 | semidirect |
| 6. C22⋊#16861593 | C2 | semidirect |
| 7. C2×#135×C257 | C2 | semidirect |
| 39. Q16×C257 | D4 | semidirect |
| 42. D8×C257 | D4 | semidirect |
| 89. C257 | #2186 | semidirect |
| 91. C2×#135 | D257 | semidirect |
| 123. Q16 | C22⋊D257 | semidirect |
| 128. D8 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551535 | 2 |
| C2×#22551533 | 2 |
| #30656973 | 2 |
| #30656541 | 2 |
| #30656538 | 2 |
| C22⋊#16861593 | 2 |
| C2×#135×C257 | 2 |
| #2186 | 257 |