Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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×#11719922 | C2 | semidirect |
| 2. C2×#13133192 | C2 | semidirect |
| 3. C2×#13133188 | C2 | semidirect |
| 4. C2×#13133139 | C2 | semidirect |
| 5. C2×#13133129 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×#102×C53 | C2 | semidirect |
| 37. C2×D4×C53 | D4 | semidirect |
| 53. C2×D212 | D4 | semidirect |
| 64. C4⋊C4×C53 | D4 | semidirect |
| 69. C4⋊Dic53 | D4 | semidirect |
| 72. C2×#88322 | D4 | semidirect |
| 94. C22×D53 | D8 | semidirect |
| 176. C2×#102 | D53 | semidirect |
| 179. C53 | #1999 | semidirect |
| 221. C2×D4 | D212 | semidirect |
| 242. C4⋊C4 | C22⋊D53 | semidirect |