Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C2×Q8×Dic251 | C2 | semidirect |
| 2. C2×#22548639 | C2 | semidirect |
| 5. #30631450 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 24. C2×SD16×C251 | C4 | semidirect |
| 73. C2×Dic251 | SD16 | semidirect |
| 86. Q8×C251 | C22⋊C4 | semidirect |
| 132. C251 | #1880 | semidirect |
| 145. C2×SD16 | Dic251 | semidirect |
| 206. Q8 | C22⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic251 | 2 |
| C2×#22548639 | 2 |
| C2×#22548636 | 2 |
| #30631590 | 2 |
| #30631450 | 2 |
| #30631441 | 2 |
| C22×SD16×C251 | 2 |
| #1880 | 251 |