Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D127 | C2 | semidirect |
| 3. C2×#16861131 | C2 | semidirect |
| 4. C2×#16861129 | C2 | semidirect |
| 5. C2×(C2×D127)⋊C8 | C2 | semidirect |
| 6. #22549638 | C2 | semidirect |
| 7. #340×C127 | C2 | semidirect |
| 14. #16861184 | C4 | semidirect |
| 36. C2×D508 | C2×C4 | semidirect |
| 52. C4⋊Dic127 | D4 | semidirect |
| 63. C4⋊C4×C127 | C2×C4 | semidirect |
| 64. C4⋊C4×C127 | D4 | semidirect |
| 130. C2×D127 | #102 | semidirect |
| 149. C127 | #1874 | semidirect |
| 156. #340 | D127 | semidirect |
| 211. C4⋊C4 | C4×D127 | semidirect |
| 212. C4⋊C4 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861184 | 2 |
| C2×C4⋊C4×D127 | 2 |
| C2×#16861131 | 2 |
| C2×#16861129 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| #22549638 | 2 |
| #340×C127 | 2 |
| #1874 | 127 |