Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C2×#97×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×#97 | D53 |
| hypocenter | C53 | C22×#97 |
| LCS | G ▷ C2×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. C2×#13133127 | C2 | semidirect |
| 5. #97×D53 | C2 | direct (N × H) |
| 6. C2×#97×C53 | C2 | semidirect |
| 10. C2×C8×D53 | C4 | semidirect |
| 16. #13133128 | C22 | semidirect |
| 17. #13133127 | C22 | semidirect |
| 20. #97×C53 | C22 | semidirect |
| 31. C2×C8×C53 | C2×C4 | semidirect |
| 38. C2×#88322 | C2×C4 | semidirect |
| 40. C8×D53 | C2×C4 | semidirect |
| 57. C8×C53 | C22×C4 | semidirect |
| 58. #88322 | C22×C4 | semidirect |
| 62. C2×D53 | #97 | direct (N × H) |
| 71. C2×C53 | C2×#97 | semidirect |
| 74. D53 | C2×#97 | direct (N × H) |
| 80. C2×#97 | D53 | direct (N × H) |
| 81. C53 | C22×#97 | semidirect |
| 95. #97 | C2×D53 | direct (N × H) |
| 109. C2×C8 | C4×D53 | semidirect |
| 133. C8 | C2×C4×D53 | semidirect |
| 146. C2 | #97×D53 | direct (N × H) |