Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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. #30632090 | C2 | semidirect |
| 3. #30632066 | C2 | semidirect |
| 4. #30632039 | C2 | semidirect |
| 5. #30632037 | C2 | semidirect |
| 7. C4×#16860800 | C2 | semidirect |
| 79. C2×C4×C251 | Q16 | semidirect |
| 104. C251 | #3170 | semidirect |
| 182. C2×C4 | #16860800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| #30632090 | 2 |
| #30632066 | 2 |
| #30632039 | 2 |
| #30632037 | 2 |
| #30631926 | 2 |
| C4×#16860800 | 2 |
| C2×C4×C251⋊C8 | 2 |
| #533×C251 | 2 |
| #3170 | 251 |