Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 3. #30631594 | C2 | semidirect |
| 4. #30631583 | C2 | semidirect |
| 5. #30631557 | C2 | semidirect |
| 7. C2×C4⋊Q8×C251 | C2 | semidirect |
| 32. C2×C4×D251 | Q8 | semidirect |
| 82. C2×D251 | C4⋊Q8 | semidirect |
| 85. C4×C251 | C22⋊Q8 | semidirect |
| 95. C251 | #2857 | semidirect |
| 97. C2×C4⋊Q8 | D251 | semidirect |
| 184. C4 | #22548691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548691 | 2 |
| C2×C42×D251 | 2 |
| #30631594 | 2 |
| #30631583 | 2 |
| #30631557 | 2 |
| #30631544 | 2 |
| C2×C4⋊Q8×C251 | 2 |
| #2857 | 251 |