Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊#87604 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C22 | C22×#87604 |
| Fitting | C24×C97 | C4 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | C24 | #87604 |
| hypocenter | C97 | C2×#99 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊#87604 | C2 | semidirect |
| 2. #15690868 | C2 | direct (N × H) |
| 6. C22⋊#87604 | C22 | semidirect |
| 10. C2×C22⋊D97 | C4 | semidirect |
| 12. C22×Dic97 | C4 | semidirect |
| 13. C24×C97 | C4 | semidirect |
| 18. C23×C97 | C2×C4 | semidirect |
| 30. C2×Dic97 | C2×C4 | semidirect |
| 50. C2×C97 | #99 | semidirect |
| 54. C97 | C2×#99 | semidirect |
| 60. C24 | #87604 | semidirect |
| 78. C23 | C2×#87604 | semidirect |
| 107. C2 | #15690868 | direct (N × H) |