Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6157 |
| commutator, socle | C22×C53 | C2×C42 |
| Fitting | C22⋊C8×C53 | C4 |
| hypercenter | C22⋊C8 | #6157 |
| hypocenter | C53 | #1752 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133271 | C2 | semidirect |
| 4. (C2×#6157)⋊C8 | C2 | semidirect |
| 7. C2×D53⋊C8 | C4 | semidirect |
| 10. C22×#88324 | C4 | semidirect |
| 17. C22⋊#88322 | C4 | semidirect |
| 18. #13133129 | C4 | semidirect |
| 19. C22⋊C8×C53 | C4 | semidirect |
| 66. #88324 | C22⋊C4 | semidirect |
| 71. C22×C53 | #97 | semidirect |
| 76. C2×D53 | #97 | semidirect |
| 98. C53 | #1752 | semidirect |
| 110. C22⋊C8 | #6157 | semidirect |
| 171. C22 | #13133271 | semidirect |