Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 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 | C22×Q8×C53 | C4 |
| hypercenter | C22×Q8 | #6157 |
| hypocenter | C53 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×#6157 | C2 | semidirect |
| 2. (C2×#6157)⋊Q8 | C2 | semidirect |
| 13. C22×Dic106 | C4 | semidirect |
| 15. C2×Q8×D53 | C4 | semidirect |
| 16. C2×Q8×D53 | C4 | semidirect |
| 20. C22×Q8×C53 | C4 | semidirect |
| 43. C22⋊#6157 | Q8 | direct (N × H) |
| 58. C2×#6157 | C2×Q8 | semidirect |
| 60. Q8×C53 | C22⋊C4 | semidirect |
| 73. Dic106 | C22⋊C4 | semidirect |
| 76. C22×C53 | C4×Q8 | semidirect |
| 82. C2×D53 | C4×Q8 | semidirect |
| 106. C53 | Q8×C22⋊C4 | semidirect |
| 113. C22×Q8 | #6157 | semidirect |
| 158. Q8 | C22⋊#6157 | direct (N × H) |
| 186. C22 | Q8×#6157 | semidirect |