Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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×#22548680 | C2 | semidirect |
| 3. #30631592 | C2 | semidirect |
| 4. #30631591 | C2 | semidirect |
| 10. C22×Dic502 | C4 | semidirect |
| 43. C22⋊Dic251 | Q8 | semidirect |
| 56. Dic502 | C22⋊C4 | semidirect |
| 67. C2×Dic251 | C2×Q8 | semidirect |
| 86. C22×C251 | C4×Q8 | semidirect |
| 105. C251 | Q8×C22⋊C4 | semidirect |
| 192. C22 | #22548680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic502 | 2 |
| C2×#22548680 | 2 |
| #30631592 | 2 |
| #30631591 | 2 |
| #30631545 | 2 |
| C22⋊C4×Dic251 | 2 |
| C4×C22⋊Dic251 | 2 |
| #380×C251 | 2 |
| Q8×C22⋊C4 | 251 |