Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C2×D4×Dic251 | C2 | semidirect |
| 2. C2×#22548636 | C2 | semidirect |
| 3. C2×#22548636 | C2 | semidirect |
| 4. #30631590 | C2 | semidirect |
| 5. #30631450 | C2 | semidirect |
| 6. #30631441 | C2 | semidirect |
| 24. C2×D8×C251 | C4 | semidirect |
| 56. C2×D4×C251 | C2×C4 | semidirect |
| 63. C2×C8×C251 | C2×C4 | semidirect |
| 76. C2×Dic251 | D8 | semidirect |
| 100. D4×C251 | C22⋊C4 | semidirect |
| 146. C251 | #1879 | semidirect |
| 160. C2×D8 | Dic251 | semidirect |
| 184. C2×D4 | C2×Dic251 | semidirect |
| 201. C2×C8 | C2×Dic251 | semidirect |
| 233. D4 | C22⋊Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic251 | 2 |
| C2×#22548636 | 2 |
| #30631590 | 2 |
| #30631450 | 2 |
| #30631441 | 2 |
| C22×D8×C251 | 2 |
| #1879 | 251 |