Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#22548734 | C2 | semidirect |
| 2. C2×#22548660 | C2 | semidirect |
| 3. C2×#22548656 | C2 | semidirect |
| 4. #30631924 | C2 | semidirect |
| 5. #30631490 | C2 | semidirect |
| 6. (C2×D251)⋊C16 | C2 | semidirect |
| 7. #357×C251 | C2 | semidirect |
| 32. Dic1004 | D4 | semidirect |
| 43. D8×C251 | D4 | semidirect |
| 89. C251 | #2186 | semidirect |
| 96. #357 | D251 | semidirect |
| 128. D8 | D1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548734 | 2 |
| C2×#22548660 | 2 |
| C2×#22548656 | 2 |
| #30631924 | 2 |
| #30631490 | 2 |
| (C2×D251)⋊C16 | 2 |
| #357×C251 | 2 |
| #2186 | 251 |