Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 3. #22549774 | C2 | semidirect |
| 4. #22549747 | C2 | semidirect |
| 5. #22549742 | C2 | semidirect |
| 6. #22549735 | C2 | semidirect |
| 7. #95×D127 | C2 | semidirect |
| 8. C4×C4⋊C4×C127 | C2 | semidirect |
| 13. C4×D508 | C4 | semidirect |
| 37. C2×C4×D127 | C2×C4 | semidirect |
| 39. C4⋊Dic127 | C2×C4 | semidirect |
| 42. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 50. C42×C127 | C2×C4 | semidirect |
| 56. D508 | C4⋊C4 | semidirect |
| 102. C127 | #2349 | semidirect |
| 109. C4×C4⋊C4 | D127 | semidirect |
| 152. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| #22549774 | 2 |
| #22549747 | 2 |
| #22549742 | 2 |
| #22549735 | 2 |
| #95×D127 | 2 |
| C4×C4⋊C4×C127 | 2 |
| #2349 | 127 |