Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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 | C53×#395 | C2 |
| hypercenter | #395 | D53 |
| hypocenter | C53 | #2388 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11719949 | C2 | semidirect |
| 2. C2×#13133179 | C2 | semidirect |
| 3. #16810540 | C2 | semidirect |
| 4. #16810534 | C2 | semidirect |
| 5. #16810533 | C2 | semidirect |
| 6. #16810470 | C2 | semidirect |
| 7. C53×#395 | C2 | semidirect |
| 38. C2×C4×D53 | D4 | semidirect |
| 52. C22×D53 | #41 | semidirect |
| 59. C2×C4×C53 | #41 | semidirect |
| 91. #395 | D53 | semidirect |
| 96. C53 | #2388 | semidirect |
| 155. C2×C4 | #11719949 | semidirect |