Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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. #30631583 | C2 | semidirect |
| 4. #30631551 | C2 | semidirect |
| 5. C4⋊C4×Dic251 | C2 | semidirect |
| 7. #30631532 | C2 | semidirect |
| 9. #22548674 | C4 | semidirect |
| 94. C251 | #2346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548674 | 2 |
| #30631583 | 2 |
| #30631581 | 2 |
| #30631551 | 2 |
| C4⋊C4×Dic251 | 2 |
| C4×C22⋊Dic251 | 2 |
| #30631532 | 2 |
| #380×C251 | 2 |
| #2346 | 251 |