Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22550224 | C2 | direct (N × H) |
| 3. C2×#16861129 | C2 | semidirect |
| 4. C2×C4×C127⋊C8 | C2 | semidirect |
| 5. C2×C4⋊Q8×C127 | C2 | semidirect |
| 12. #16861129 | C22 | semidirect |
| 13. C4×C127⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C127 | C22 | semidirect |
| 74. C2×C127 | #486 | semidirect |
| 80. C127 | C2×#486 | semidirect |
| 81. C2×C4⋊Q8 | D127 | semidirect |
| 92. C4⋊Q8 | C2×D127 | semidirect |
| 155. C2 | #22550224 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861206 | 2 |
| #22550224 | 2 |
| C2×#16861129 | 2 |
| C2×C4×C127⋊C8 | 2 |
| C2×C4⋊Q8×C127 | 2 |
| C2×#486 | 127 |