Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
848 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22548635 | C2 | semidirect |
| 3. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 4. #380×C251 | C2 | semidirect |
| 9. C22×D1004 | C4 | semidirect |
| 11. C22×C251⋊C8 | C22 | semidirect |
| 15. C2×C4⋊C4×C251 | C22 | semidirect |
| 56. D1004 | C22⋊C4 | semidirect |
| 78. C22×C251 | #102 | semidirect |
| 101. C251 | #1786 | semidirect |
| 106. #380 | D251 | semidirect |
| 115. C2×C4⋊C4 | C2×D251 | semidirect |
| 186. C22 | #22548635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D1004 | 2 |
| C2×#22548635 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| #380×C251 | 2 |
| #1786 | 251 |