Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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×#16861131 | C2 | semidirect |
| 3. C2×#16861130 | C2 | semidirect |
| 4. C2×#16861129 | C2 | semidirect |
| 5. #22549775 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 7. C2×#102×C127 | C2 | semidirect |
| 62. C4⋊C4×C127 | D4 | semidirect |
| 147. C127 | #2041 | semidirect |
| 152. C2×#102 | D127 | semidirect |
| 207. C4⋊C4 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861205 | 2 |
| C2×#16861131 | 2 |
| C2×#16861130 | 2 |
| C2×#16861129 | 2 |
| #22549775 | 2 |
| #22549630 | 2 |
| C2×#102×C127 | 2 |
| #2041 | 127 |