Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
480 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 309 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. C2×#13133153 | C2 | direct (N × H) |
| 7. #13133153 | C22 | direct (N × H) |
| 42. C22×C53 | #108 | semidirect |
| 53. C2×C53 | C2×#108 | semidirect |
| 58. C53 | C22×#108 | semidirect |
| 97. C22 | #13133153 | direct (N × H) |
| 107. C2 | C2×#13133153 | direct (N × H) |