Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22548748 | C2 | semidirect |
| 3. C2×#22548715 | C2 | semidirect |
| 4. #30632081 | C2 | semidirect |
| 5. #30632067 | C2 | semidirect |
| 6. #30632060 | C2 | semidirect |
| 7. C4×M16×C251 | C2 | semidirect |
| 44. M16×C251 | D4 | semidirect |
| 75. C4×C251 | #137 | semidirect |
| 83. C251 | #3152 | semidirect |
| 91. C4×M16 | D251 | semidirect |
| 124. M16 | D1004 | semidirect |
| 161. C4 | #22548748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548748 | 2 |
| #30632237 | 2 |
| C2×#22548715 | 2 |
| #30632081 | 2 |
| #30632067 | 2 |
| #30632060 | 2 |
| C4×M16×C251 | 2 |
| #3152 | 251 |