Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×#13133280 | C2 | direct (N × H) |
| 11. #13133280 | C22 | direct (N × H) |
| 13. C22×Dic106 | C4 | semidirect |
| 16. C2×Q8×D53 | C4 | semidirect |
| 20. C22×Q8×C53 | C4 | semidirect |
| 25. C2×Q8×C53 | C2×C4 | semidirect |
| 33. Q8×D53 | C2×C4 | semidirect |
| 44. C2×Dic106 | C2×C4 | semidirect |
| 58. Q8×C53 | C22×C4 | semidirect |
| 75. Dic106 | C22×C4 | semidirect |
| 77. C22×C53 | #103 | semidirect |
| 79. C2×D53 | #103 | semidirect |
| 92. C2×C53 | C2×#103 | semidirect |
| 94. D53 | C2×#103 | semidirect |
| 101. C53 | C22×#103 | semidirect |
| 108. C22×Q8 | #6157 | semidirect |
| 129. C2×Q8 | C2×#6157 | semidirect |
| 157. Q8 | C22×#6157 | semidirect |
| 179. C22 | #13133280 | direct (N × H) |
| 191. C2 | C2×#13133280 | direct (N × H) |