Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#97×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×#97 | D53 |
| hypocenter | C53 | #1749 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#13133128 | C2 | semidirect |
| 4. #16810377 | C2 | semidirect |
| 5. C2×#97×C53 | C2 | semidirect |
| 13. #13133129 | C4 | semidirect |
| 32. C2×C8×C53 | C2×C4 | semidirect |
| 40. C2×#88322 | C2×C4 | semidirect |
| 74. C2×D53 | #97 | semidirect |
| 90. C2×#97 | D53 | semidirect |
| 92. C53 | #1749 | semidirect |
| 122. C2×C8 | C4×D53 | semidirect |