Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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×#22551523 | C2 | semidirect |
| 4. #30656499 | C2 | semidirect |
| 12. C22⋊#14523339 | C4 | semidirect |
| 24. C2×#14523339 | C2×C4 | semidirect |
| 74. C22×C257 | #106 | semidirect |
| 96. C257 | #1853 | semidirect |
| 171. C22 | #22551523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic257 | 2 |
| C2×#22551523 | 2 |
| C2×C22⋊#14523339 | 2 |
| #30656499 | 2 |
| #380×C257 | 2 |
| #1853 | 257 |