Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #22549780 | C2 | semidirect |
| 3. #22549767 | C2 | semidirect |
| 4. #22549765 | C2 | semidirect |
| 6. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 7. #22549723 | C2 | semidirect |
| 8. #22549722 | C2 | semidirect |
| 9. #376×C127 | C2 | semidirect |
| 13. #16861197 | C4 | semidirect |
| 35. C2×Dic254 | C2×C4 | semidirect |
| 49. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 50. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 59. C42×C127 | C2×C4 | semidirect |
| 120. C127 | #2372 | semidirect |
| 129. #376 | D127 | semidirect |
| 179. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861197 | 2 |
| #22549780 | 2 |
| #22549767 | 2 |
| #22549765 | 2 |
| #22549754 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| #22549723 | 2 |
| #22549722 | 2 |
| #376×C127 | 2 |
| #2372 | 127 |