Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1008 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#6157 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C22 | C23×#6157 |
| Fitting | C25×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C25 | #6157 |
| hypocenter | C53 | C2×#407 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719940 | C2 | semidirect |
| 2. #16811593 | C2 | direct (N × H) |
| 3. C2×C22⋊#88324 | C2 | semidirect |
| 6. C2×#11719940 | C22 | semidirect |
| 7. C22×#88324 | C22 | semidirect |
| 8. C22⋊#88324 | C22 | semidirect |
| 39. C2×#88324 | C23 | semidirect |
| 47. C23×C53 | M16 | semidirect |
| 74. C22×C53 | C2×M16 | semidirect |
| 83. C2×C53 | #407 | semidirect |
| 90. C53 | C2×#407 | semidirect |
| 132. C23 | #11719940 | semidirect |
| 160. C22 | C2×#11719940 | semidirect |
| 168. C2 | #16811593 | direct (N × H) |