Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C23×D103 |
| commutator | C2×C103 | C23×C4 |
| Fitting | C4×D4×C103 | C2 |
| socle | C22×C103 | C24 |
| hypercenter | C4×D4 | D103 |
| hypocenter | C103 | #520 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic206 | C2 | semidirect |
| 3. #15692986 | C2 | semidirect |
| 4. D4×Dic103 | C2 | semidirect |
| 5. C4×C22⋊D103 | C2 | semidirect |
| 6. (C22⋊D103)⋊C4 | C2 | semidirect |
| 7. #15692978 | C2 | semidirect |
| 8. #15692977 | C2 | semidirect |
| 9. C2×Dic103⋊C4 | C2 | semidirect |
| 10. C4⋊C4×D103 | C2 | semidirect |
| 11. C4×D4×C103 | C2 | semidirect |
| 12. #13110104 | C4 | semidirect |
| 38. D4×C103 | C2×C4 | semidirect |
| 44. C22⋊D103 | C2×C4 | semidirect |
| 46. C2×Dic103 | C2×C4 | semidirect |
| 53. C4×D103 | C2×C4 | semidirect |
| 54. Dic206 | C2×C4 | semidirect |
| 76. C103 | #520 | semidirect |
| 84. C4×D4 | D103 | semidirect |
| 117. D4 | C4×D103 | semidirect |