Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1104 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 309 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. C2×#16861168 | C2 | semidirect |
| 2. #22549779 | C2 | semidirect |
| 3. #22549732 | C2 | semidirect |
| 6. C2×C4⋊Dic127 | C22 | semidirect |
| 8. C2×C22⋊Dic127 | C22 | semidirect |
| 9. C2×C4×Dic127 | C22 | semidirect |
| 12. C22×D4×C127 | C4 | semidirect |
| 45. C2×C4×C127 | C22⋊C4 | semidirect |
| 67. C127 | #2309 | semidirect |
| 74. C22×D4 | Dic127 | semidirect |
| 112. C2×C4 | C22⋊Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861168 | 2 |
| #22549779 | 2 |
| #22549732 | 2 |
| C23×D4×C127 | 2 |
| #2309 | 127 |