Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4 | C22×D53 |
| commutator | C22×C53 | C2×C42 |
| Fitting | C2×C22⋊C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D53 |
| hypocenter | C53 | #1752 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133127 | C2 | semidirect |
| 4. #16810377 | C2 | semidirect |
| 7. C22×#88322 | C4 | semidirect |
| 16. C22⋊C8×C53 | C4 | semidirect |
| 55. #88322 | C22⋊C4 | semidirect |
| 59. C22×C53 | #97 | semidirect |
| 80. C53 | #1752 | semidirect |
| 89. C22⋊C8 | Dic53 | semidirect |
| 134. C22 | #13133127 | semidirect |