Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13133191 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×#121×C53 | C2 | semidirect |
| 40. C2×D4×C53 | D4 | semidirect |
| 59. C2×D212 | D4 | semidirect |
| 61. C4⋊C4×C53 | D4 | semidirect |
| 66. C4⋊Dic53 | D4 | semidirect |
| 72. C2×#88322 | D4 | semidirect |
| 86. C23×C53 | D8 | semidirect |
| 174. C2×#121 | D53 | semidirect |
| 179. C53 | #1999 | semidirect |
| 221. C2×D4 | C22⋊D53 | semidirect |
| 242. C4⋊C4 | C22⋊D53 | semidirect |
| 265. C23 | #11719922 | semidirect |