Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 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. C2×#22548639 | C2 | direct (N × H) |
| 10. #22548639 | C22 | direct (N × H) |
| 13. C22×Q8×C251 | C4 | semidirect |
| 27. C2×Q8×C251 | C2×C4 | semidirect |
| 44. Q8×C251 | C22×C4 | semidirect |
| 52. C22×C251 | #103 | semidirect |
| 62. C2×C251 | C2×#103 | semidirect |
| 66. C251 | C22×#103 | semidirect |
| 74. C22×Q8 | Dic251 | semidirect |
| 88. C2×Q8 | C2×Dic251 | semidirect |
| 108. Q8 | C22×Dic251 | semidirect |
| 119. C22 | #22548639 | direct (N × H) |
| 129. C2 | C2×#22548639 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C251⋊C8 | 2 |
| C22×C4⋊Dic251 | 2 |
| C2×#22548639 | 2 |
| C23×Q8×C251 | 2 |
| C22×#103 | 251 |