Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D53 |
| commutator | C23×C53 | C22×C4 |
| Fitting | C2×#95×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C2×#95 | D53 |
| hypocenter | C53 | #1438 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11719921 | C2 | semidirect |
| 3. C2×#13133124 | C2 | semidirect |
| 4. C2×#95×C53 | C2 | semidirect |
| 9. C22×D212 | C4 | semidirect |
| 36. C22×C4×C53 | D4 | semidirect |
| 41. C22×Dic53 | D4 | semidirect |
| 75. C22×D53 | C22⋊C4 | semidirect |
| 84. C2×C4×C53 | C22⋊C4 | semidirect |
| 132. C2×#95 | D53 | semidirect |
| 133. C53 | #1438 | semidirect |
| 173. C22×C4 | D212 | semidirect |
| 219. C2×C4 | #11719921 | semidirect |