Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16861143 | C2 | semidirect |
| 4. #22549638 | C2 | semidirect |
| 5. C2×#106×C127 | C2 | semidirect |
| 9. C2×#14523231 | C4 | semidirect |
| 67. C8×C127 | C22⋊C4 | semidirect |
| 92. C127 | #1809 | semidirect |
| 95. C2×#106 | D127 | semidirect |
| 159. C8 | (C2×D127)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523231 | 2 |
| C2×#16861143 | 2 |
| #22549733 | 2 |
| #22549638 | 2 |
| C2×#106×C127 | 2 |
| #1809 | 127 |