Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C2×C22⋊C4×C53 | C4 |
| hypercenter | C2×C22⋊C4 | #6157 |
| hypocenter | C53 | #2973 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811652 | C2 | semidirect |
| 2. #16811644 | C2 | semidirect |
| 3. #16811594 | C2 | semidirect |
| 4. C2×C22⋊#88324 | C2 | semidirect |
| 6. C2×#11719936 | C22 | semidirect |
| 7. C22×#88324 | C22 | semidirect |
| 8. C4⋊#88324 | C22 | semidirect |
| 9. #13133274 | C22 | semidirect |
| 11. C22⋊#88324 | C22 | semidirect |
| 12. #13133272 | C22 | semidirect |
| 47. C23×C53 | M16 | semidirect |
| 101. C53 | #2973 | semidirect |
| 147. C23 | #11719936 | semidirect |