Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
944 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator, socle | C23×C53 | C24 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×#41×C53 | C2 |
| hypercenter | C22×#41 | D53 |
| hypocenter | C53 | #2388 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C22⋊D53 | C2 | semidirect |
| 2. #16810542 | C2 | semidirect |
| 3. #16810537 | C2 | semidirect |
| 4. #16810534 | C2 | semidirect |
| 5. #16810531 | C2 | semidirect |
| 6. C4×C22⋊Dic53 | C2 | semidirect |
| 7. C22×#41×C53 | C2 | semidirect |
| 29. C22×C4×C53 | D4 | semidirect |
| 52. C22×D53 | #41 | semidirect |
| 65. C2×Dic53 | #41 | semidirect |
| 89. C22×#41 | D53 | semidirect |
| 96. C53 | #2388 | semidirect |
| 125. C22×C4 | C22⋊D53 | semidirect |