Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#87604 |
| commutator | C2×C97 | C23×C4 |
| Frattini | C2 | C23×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C2×#117 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690889 | C2 | direct (N × H) |
| 2. C2×C4⋊#87604 | C2 | semidirect |
| 4. C2×C4×#87604 | C2 | semidirect |
| 7. C4⋊#87604 | C22 | semidirect |
| 9. C4×#87604 | C22 | semidirect |
| 11. C22×Dic97 | C4 | semidirect |
| 12. C2×C4×D97 | C4 | semidirect |
| 13. C2×C4×D97 | C4 | semidirect |
| 14. C2×C4×D97 | C4 | semidirect |
| 18. C22×C4×C97 | C4 | semidirect |
| 29. C2×C4×C97 | C2×C4 | semidirect |
| 32. C2×Dic97 | C2×C4 | semidirect |
| 35. C4×D97 | C2×C4 | semidirect |
| 36. C4×D97 | C2×C4 | semidirect |
| 55. C2×C97 | #117 | semidirect |
| 58. D97 | #117 | semidirect |
| 60. C97 | C2×#117 | semidirect |
| 76. C22×C4 | #87604 | semidirect |
| 99. C2×C4 | C2×#87604 | semidirect |
| 119. C2 | #15690889 | direct (N × H) |