Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548709 | C2 | semidirect |
| 3. #30631582 | C2 | semidirect |
| 4. #30631581 | C2 | semidirect |
| 5. #30631577 | C2 | semidirect |
| 6. C42×Dic251 | C2 | semidirect |
| 7. C2×#126×C251 | C2 | semidirect |
| 39. C42×C251 | D4 | semidirect |
| 74. Dic251 | #126 | semidirect |
| 80. C251 | #2860 | semidirect |
| 83. C2×#126 | D251 | semidirect |
| 120. C42 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548709 | 2 |
| #30631587 | 2 |
| #30631582 | 2 |
| #30631581 | 2 |
| #30631577 | 2 |
| C42×Dic251 | 2 |
| C2×#126×C251 | 2 |
| #2860 | 251 |