Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #30632089 | C2 | semidirect |
| 3. #30632088 | C2 | semidirect |
| 4. #30632087 | C2 | semidirect |
| 5. #30632086 | C2 | semidirect |
| 9. #499×C251 | C2 | semidirect |
| 75. D251 | #499 | direct (N × H) |
| 76. C251 | C2×#499 | semidirect |
| 83. #499 | D251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D251 | 2 |
| #30632089 | 2 |
| #30632088 | 2 |
| #30632087 | 2 |
| #30632086 | 2 |
| #107×D251 | 2 |
| #106×D251 | 2 |
| C4×C8×D251 | 2 |
| #499×C251 | 2 |
| C2×#499 | 251 |