Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #30656479 | C2 | semidirect |
| 4. #30656478 | C2 | semidirect |
| 5. #330×C257 | C2 | semidirect |
| 57. C257 | #1526 | semidirect |
| 63. #330 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657293 | 2 |
| #30656689 | 2 |
| #30656479 | 2 |
| #30656478 | 2 |
| #330×C257 | 2 |
| #1526 | 257 |