Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C22⋊D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #131×C97 | C2 |
| socle | C2×C97 | C4×D4 |
| hypercenter | #131 | D97 |
| hypocenter | C97 | #444 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15690816 | C2 | semidirect |
| 3. #15690745 | C2 | semidirect |
| 4. #15690737 | C2 | semidirect |
| 5. #15690736 | C2 | semidirect |
| 6. #15690720 | C2 | semidirect |
| 7. #131×C97 | C2 | semidirect |
| 9. #13095501 | C4 | semidirect |
| 10. #13095499 | C4 | semidirect |
| 11. #13095498 | C4 | semidirect |
| 12. #13095496 | C4 | semidirect |
| 51. C97 | #444 | semidirect |
| 55. #131 | D97 | semidirect |