Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×Dic212 | C2 | semidirect |
| 3. #16810864 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133142 | C2 | semidirect |
| 9. C2×Dic212 | C22 | semidirect |
| 15. #13133151 | C22 | semidirect |
| 16. #13133142 | C22 | semidirect |
| 47. C23×C53 | Q16 | semidirect |
| 73. C22×C53 | C2×Q16 | semidirect |
| 84. C2×C53 | #467 | semidirect |
| 94. C53 | C2×#467 | semidirect |
| 135. C23 | Dic212 | semidirect |
| 161. C22 | C2×Dic212 | semidirect |
| 171. C2 | #16810864 | direct (N × H) |