Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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×D388 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #117×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #117 | D97 |
| hypocenter | C97 | #421 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13095495 | C2 | semidirect |
| 3. #15690738 | C2 | semidirect |
| 4. #117×C97 | C2 | semidirect |
| 7. #13095511 | C4 | semidirect |
| 9. C2×Dic194 | C4 | semidirect |
| 10. C2×D388 | C4 | semidirect |
| 14. #13095495 | C22 | semidirect |
| 19. C42×C97 | C22 | semidirect |
| 56. C97 | #421 | semidirect |
| 60. #117 | D97 | semidirect |
| 76. C42 | C2×D97 | semidirect |