Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22551581 | C2 | semidirect |
| 3. C2×#22551519 | C2 | semidirect |
| 4. #30656746 | C2 | semidirect |
| 5. C2×#22551508 | C2 | semidirect |
| 6. #30656498 | C2 | semidirect |
| 7. C2×#137×C257 | C2 | semidirect |
| 47. C4×Dic257 | D4 | semidirect |
| 58. C2×Q8×C257 | D4 | semidirect |
| 67. M16×C257 | D4 | semidirect |
| 131. C257 | #2004 | semidirect |
| 133. C2×#137 | D257 | semidirect |
| 172. C2×Q8 | C22⋊D257 | semidirect |
| 191. M16 | C22⋊D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657301 | 2 |
| C2×#22551581 | 2 |
| C2×#22551519 | 2 |
| #30656746 | 2 |
| C2×#22551508 | 2 |
| #30656498 | 2 |
| C2×#137×C257 | 2 |
| #2004 | 257 |