Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #41×Dic251 | C2 | semidirect |
| 2. #30631799 | C2 | semidirect |
| 3. #30631794 | C2 | semidirect |
| 4. #30631788 | C2 | semidirect |
| 5. #30631725 | C2 | semidirect |
| 6. #30631683 | C2 | semidirect |
| 7. C2×#22548625 | C2 | semidirect |
| 24. #135×C251 | C4 | semidirect |
| 42. #41×C251 | C2×C4 | semidirect |
| 48. Q16×C251 | C2×C4 | semidirect |
| 49. SD16×C251 | C2×C4 | semidirect |
| 50. D8×C251 | C2×C4 | semidirect |
| 51. C2×C8×C251 | C2×C4 | semidirect |
| 89. C251 | #2943 | semidirect |
| 100. #135 | Dic251 | semidirect |
| 120. #41 | C2×Dic251 | semidirect |
| 128. Q16 | C2×Dic251 | semidirect |
| 129. SD16 | C2×Dic251 | semidirect |
| 130. D8 | C2×Dic251 | semidirect |
| 133. C2×C8 | C2×Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic251 | 2 |
| #30631799 | 2 |
| #30631794 | 2 |
| #30631788 | 2 |
| #30631725 | 2 |
| #30631683 | 2 |
| C2×#22548625 | 2 |
| C2×#135×C251 | 2 |
| #2943 | 251 |