Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 186 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 | C2×C4⋊C4×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4⋊C4 | #6157 |
| hypocenter | C53 | C2×#435 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
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. #16811653 | C2 | direct (N × H) |
| 4. C2×#13133284 | C2 | semidirect |
| 5. C2×#13133274 | C2 | semidirect |
| 6. C2×#13133274 | C2 | semidirect |
| 7. C2×#13133272 | C2 | semidirect |
| 10. C2×#11719936 | C22 | semidirect |
| 12. C2×D53⋊C8 | C22 | semidirect |
| 17. #13133284 | C22 | semidirect |
| 18. #13133274 | C22 | semidirect |
| 19. #13133274 | C22 | semidirect |
| 20. #13133272 | C22 | semidirect |
| 50. C2×#88324 | D4 | semidirect |
| 68. C22×D53 | M16 | semidirect |
| 93. #88324 | C2×D4 | semidirect |
| 105. C2×D53 | C2×M16 | semidirect |
| 114. C2×C53 | #435 | semidirect |
| 128. C53 | C2×#435 | semidirect |
| 235. C2 | #16811653 | direct (N × H) |