Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#22548651 | C2 | semidirect |
| 4. #30631456 | C2 | semidirect |
| 5. C2×#106×C251 | C2 | semidirect |
| 8. #22548721 | C4 | semidirect |
| 84. C251 | #1815 | semidirect |
| 88. C2×#106 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548721 | 2 |
| C2×#22548651 | 2 |
| #30631686 | 2 |
| #30631456 | 2 |
| C2×#106×C251 | 2 |
| #1815 | 251 |