Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#14523235 | C2 | semidirect |
| 3. C2×#16861129 | C2 | semidirect |
| 4. #22549631 | C2 | semidirect |
| 5. #391×C127 | C2 | semidirect |
| 31. C2×C127⋊C8 | D4 | semidirect |
| 35. C2×Q8×C127 | D4 | semidirect |
| 63. C2×C4×C127 | SD16 | semidirect |
| 90. C127 | #2014 | semidirect |
| 94. #391 | D127 | semidirect |
| 112. C2×Q8 | D508 | semidirect |
| 152. C2×C4 | #14523235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| C2×#16861206 | 2 |
| C2×#16861129 | 2 |
| #22549631 | 2 |
| #391×C127 | 2 |
| #2014 | 127 |