Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic254 | C2 | semidirect |
| 3. #16861242 | C2 | direct (N × H) |
| 4. C2×Dic508 | C2 | semidirect |
| 5. C2×#14523237 | C2 | semidirect |
| 6. C2×M16×C127 | C2 | semidirect |
| 13. C2×Dic254 | C22 | semidirect |
| 18. Dic508 | C22 | semidirect |
| 19. #14523237 | C22 | semidirect |
| 21. M16×C127 | C22 | semidirect |
| 53. C2×C127 | #137 | semidirect |
| 56. C127 | C2×#137 | semidirect |
| 63. C2×M16 | D127 | semidirect |
| 78. M16 | C2×D127 | semidirect |
| 111. C2 | #16861242 | direct (N × H) |