Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 13. #22551521 | C4 | semidirect |
| 15. C8×Dic257 | C4 | semidirect |
| 65. C8×C257 | C4⋊C4 | semidirect |
| 78. Dic257 | #97 | semidirect |
| 84. C257 | #1770 | semidirect |
| 150. C8 | #16861597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551521 | 2 |
| C2×#22551502 | 2 |
| C2×C8×Dic257 | 2 |
| C4×#16861597 | 2 |
| #30656492 | 2 |
| #30656491 | 2 |
| C2×#97×C257 | 2 |
| #1770 | 257 |