Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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. M32×D127 | C2 | semidirect |
| 3. #22549658 | C2 | semidirect |
| 4. #22549657 | C2 | semidirect |
| 5. #349×C127 | C2 | semidirect |
| 83. C127 | #2115 | semidirect |
| 88. #349 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861217 | 2 |
| M32×D127 | 2 |
| #22549658 | 2 |
| #22549657 | 2 |
| #349×C127 | 2 |
| #2115 | 127 |