Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 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×Q8×Dic127 | C2 | semidirect |
| 3. #22549778 | C2 | semidirect |
| 4. #22549777 | C2 | semidirect |
| 5. #22549733 | C2 | semidirect |
| 6. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 7. C2×C4×Q8×C127 | C2 | semidirect |
| 10. C2×#14523249 | C4 | semidirect |
| 65. C2×Dic127 | #41 | semidirect |
| 68. Q8×C127 | C22⋊C4 | semidirect |
| 77. C2×C4×C127 | #41 | semidirect |
| 107. C127 | #2341 | semidirect |
| 110. C2×C4×Q8 | D127 | semidirect |
| 164. Q8 | (C2×D127)⋊C4 | semidirect |
| 184. C2×C4 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523249 | 2 |
| C2×Q8×Dic127 | 2 |
| #22549778 | 2 |
| #22549777 | 2 |
| #22549733 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C2×C4×Q8×C127 | 2 |
| #2341 | 127 |