Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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 | C22×Q8×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C22×Q8 | #6157 |
| hypocenter | C53 | C2×#408 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719936 | C2 | semidirect |
| 2. C22×D53⋊C8 | C2 | semidirect |
| 3. #16811598 | C2 | direct (N × H) |
| 4. C2×#13133274 | C2 | semidirect |
| 7. C2×#11719936 | C22 | semidirect |
| 9. C2×D53⋊C8 | C22 | semidirect |
| 12. #13133274 | C22 | semidirect |
| 91. C2×C53 | #408 | semidirect |
| 101. C53 | C2×#408 | semidirect |
| 188. C2 | #16811598 | direct (N × H) |