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. #30632155 | C2 | semidirect |
| 3. #30631703 | C2 | semidirect |
| 4. C2×#22548641 | C2 | semidirect |
| 5. #30631660 | C2 | semidirect |
| 6. #30631448 | C2 | semidirect |
| 7. #344×C251 | C2 | semidirect |
| 11. #22548748 | C4 | semidirect |
| 13. #22548743 | C4 | semidirect |
| 37. C2×Dic502 | C2×C4 | semidirect |
| 39. C2×D1004 | C2×C4 | semidirect |
| 64. M16×C251 | C2×C4 | semidirect |
| 129. C251 | #1906 | semidirect |
| 136. #344 | D251 | semidirect |
| 185. M16 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| #30632155 | 2 |
| #30631703 | 2 |
| C2×#22548641 | 2 |
| #30631660 | 2 |
| #30631448 | 2 |
| #344×C251 | 2 |
| #1906 | 251 |