Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C2×#121×C53 | C2 |
| hypercenter | C2×#121 | D53 |
| hypocenter | C53 | #2431 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719945 | C2 | semidirect |
| 2. C2×#13133213 | C2 | semidirect |
| 3. C2×#13133204 | C2 | semidirect |
| 4. #16810531 | C2 | semidirect |
| 5. #16810528 | C2 | semidirect |
| 6. #16810524 | C2 | semidirect |
| 7. #16810499 | C2 | semidirect |
| 8. C4×C22⋊Dic53 | C2 | semidirect |
| 9. C2×#121×C53 | C2 | semidirect |
| 43. C22×C4×C53 | D4 | semidirect |
| 59. C2×D212 | D4 | semidirect |
| 65. C2×Dic106 | D4 | semidirect |
| 110. C2×Dic53 | #41 | semidirect |
| 152. C2×#121 | D53 | semidirect |
| 158. C53 | #2431 | semidirect |
| 211. C22×C4 | C22⋊D53 | semidirect |