Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D103 |
| commutator | C4×C103 | C22×C4 |
| Frattini | C2×C4 | C22×D103 |
| Fitting | #104×C103 | C2 |
| socle | C2×C103 | C4×D4 |
| hypercenter | #104 | D103 |
| hypocenter | C103 | #443 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15693029 | C2 | semidirect |
| 3. #15693028 | C2 | semidirect |
| 4. #15692956 | C2 | semidirect |
| 5. #15692949 | C2 | semidirect |
| 6. C4×C103⋊C8 | C2 | semidirect |
| 7. #104×C103 | C2 | semidirect |
| 9. #13110095 | C4 | semidirect |
| 10. #13110093 | C4 | semidirect |
| 11. #13110092 | C4 | semidirect |
| 12. #13110090 | C4 | semidirect |
| 51. C103 | #443 | semidirect |
| 58. #104 | D103 | semidirect |