Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13133160 | C2 | semidirect |
| 3. C4⋊#11719908 | C2 | semidirect |
| 4. #16810423 | C2 | semidirect |
| 5. C4×Q16×C53 | C2 | semidirect |
| 21. Q16×C53 | D4 | semidirect |
| 54. C4×C53 | SD32 | semidirect |
| 64. C4×Q16 | D53 | semidirect |
| 67. C53 | #2207 | semidirect |
| 83. Q16 | D212 | semidirect |
| 116. C4 | #13133160 | semidirect |