Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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×Q8×Dic251 | C2 | semidirect |
| 3. #30631589 | C2 | semidirect |
| 4. #30631588 | C2 | semidirect |
| 5. #30631544 | C2 | semidirect |
| 6. C4×(C2×D251)⋊C4 | C2 | semidirect |
| 7. C2×C4×Q8×C251 | C2 | semidirect |
| 10. C2×#16860811 | C4 | semidirect |
| 65. C2×Dic251 | #41 | semidirect |
| 68. Q8×C251 | C22⋊C4 | semidirect |
| 77. C2×C4×C251 | #41 | semidirect |
| 106. C251 | #2341 | semidirect |
| 110. C2×C4×Q8 | D251 | semidirect |
| 164. Q8 | (C2×D251)⋊C4 | semidirect |
| 184. C2×C4 | #16860811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860811 | 2 |
| C2×Q8×Dic251 | 2 |
| #30631589 | 2 |
| #30631588 | 2 |
| #30631544 | 2 |
| C4×(C2×D251)⋊C4 | 2 |
| C2×C4×Q8×C251 | 2 |
| #2341 | 251 |