Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#16860810 | C2 | semidirect |
| 3. #30631703 | C2 | semidirect |
| 4. #30631661 | C2 | semidirect |
| 5. #30631458 | C2 | semidirect |
| 6. #30631447 | C2 | semidirect |
| 7. C2×#104×C251 | C2 | semidirect |
| 9. #22548746 | C4 | semidirect |
| 11. #22548741 | C4 | semidirect |
| 43. #16860794 | C2×C4 | semidirect |
| 58. C2×Q8×C251 | C2×C4 | semidirect |
| 60. C2×D4×C251 | C2×C4 | semidirect |
| 129. C251 | #1906 | semidirect |
| 134. C2×#104 | D251 | semidirect |
| 168. C2×Q8 | C4×D251 | semidirect |
| 172. C2×D4 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632485 | 2 |
| C4×#16860810 | 2 |
| #30631703 | 2 |
| #30631661 | 2 |
| #30631458 | 2 |
| #30631447 | 2 |
| C2×#104×C251 | 2 |
| #1906 | 251 |