Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22550357 | C2 | semidirect |
| 3. #22549975 | C2 | semidirect |
| 4. #22549970 | C2 | semidirect |
| 5. #22549958 | C2 | semidirect |
| 6. #22549875 | C2 | semidirect |
| 7. #22549831 | C2 | semidirect |
| 8. C2×#107×C127 | C2 | semidirect |
| 10. #16861231 | C4 | semidirect |
| 30. #14523248 | C2×C4 | semidirect |
| 36. Dic508 | C2×C4 | semidirect |
| 37. #14523237 | C2×C4 | semidirect |
| 38. D1016 | C2×C4 | semidirect |
| 50. C2×C8×C127 | C2×C4 | semidirect |
| 96. C127 | #2951 | semidirect |
| 102. C2×#107 | D127 | semidirect |
| 139. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| #22550357 | 2 |
| #22549975 | 2 |
| #22549970 | 2 |
| #22549958 | 2 |
| #22549875 | 2 |
| #22549831 | 2 |
| C2×#107×C127 | 2 |
| #2951 | 127 |