Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
488 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 245 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. Q16×Dic251 | C2 | direct (N × H) |
| 18. C2×Q16×C251 | C4 | semidirect |
| 38. Q16×C251 | C2×C4 | semidirect |
| 44. C2×Dic251 | Q16 | direct (N × H) |
| 69. Dic251 | C2×Q16 | direct (N × H) |
| 70. C2×C251 | C4×Q16 | semidirect |
| 74. C251 | C2×C4×Q16 | semidirect |
| 83. C2×Q16 | Dic251 | direct (N × H) |
| 105. Q16 | C2×Dic251 | direct (N × H) |
| 145. C2 | Q16×Dic251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic251 | 2 |
| Q16×Dic251 | 2 |
| C2×#22548649 | 2 |
| C2×#22548639 | 2 |
| C2×C8×Dic251 | 2 |
| C22×Q16×C251 | 2 |
| C2×C4×Q16 | 251 |