Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×#14523235 | C2 | semidirect |
| 2. C22×C127⋊C8 | C2 | semidirect |
| 4. #16861140 | C2 | semidirect |
| 5. #16861133 | C2 | semidirect |
| 6. #16861129 | C2 | semidirect |
| 7. C22⋊Q8×C127 | C2 | semidirect |
| 27. C127⋊C8 | D4 | semidirect |
| 39. C22×C127 | SD16 | semidirect |
| 55. C127 | #465 | semidirect |
| 59. C22⋊Q8 | D127 | semidirect |
| 98. C22 | #14523235 | semidirect |