Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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×#22548639 | C2 | semidirect |
| 5. #30631449 | C2 | semidirect |
| 6. #30631442 | C2 | semidirect |
| 7. C2×C4×Q8×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 82. Q8×C251 | C22⋊C4 | semidirect |
| 94. C2×C4×C251 | SD16 | semidirect |
| 132. C251 | #1880 | semidirect |
| 135. C2×C4×Q8 | D251 | semidirect |
| 206. Q8 | (C2×D251)⋊C4 | semidirect |
| 225. C2×C4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860797 | 2 |
| C2×#22548639 | 2 |
| C2×#22548635 | 2 |
| #30631589 | 2 |
| #30631449 | 2 |
| #30631442 | 2 |
| C2×C4×Q8×C251 | 2 |
| #1880 | 251 |