Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. #30632065 | C2 | direct (N × H) |
| 49. C2×Dic251 | Q16 | semidirect |
| 71. Dic251 | C2×Q16 | semidirect |
| 72. C2×C251 | #494 | semidirect |
| 75. C251 | C2×#494 | semidirect |
| 148. C2 | #30632065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic1004 | 2 |
| C22×#16860800 | 2 |
| C2×#22548713 | 2 |
| #30632065 | 2 |
| C2×C8×Dic251 | 2 |
| C22×Q16×C251 | 2 |
| C2×#494 | 251 |