Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 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 | C4×Q8×C53 | C4 |
| hypercenter | C4×Q8 | #6157 |
| hypocenter | C53 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. Q8×Dic53 | C4 | semidirect |
| 15. C4×Dic106 | C4 | semidirect |
| 16. #13133182 | C4 | semidirect |
| 19. C4×Q8×C53 | C4 | semidirect |
| 32. C4⋊#6157 | Q8 | direct (N × H) |
| 48. Q8×C53 | C4⋊C4 | semidirect |
| 61. Dic106 | C4⋊C4 | semidirect |
| 73. C4×C53 | C4×Q8 | semidirect |
| 76. Dic53 | C4×Q8 | semidirect |
| 90. C53 | Q8×C4⋊C4 | semidirect |
| 96. C4×Q8 | #6157 | semidirect |
| 128. Q8 | C4⋊#6157 | direct (N × H) |
| 161. C4 | Q8×#6157 | semidirect |