Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 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 | C2×C42 |
| Frattini | C22 | C22×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C4×C22⋊C4 |
| 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 |
|---|---|---|
| 2. C2×C4×#87604 | C2 | semidirect |
| 3. (C2×#87604)⋊C4 | C2 | semidirect |
| 6. C22⋊#87604 | C4 | direct (N × H) |
| 9. C22×Dic97 | C4 | semidirect |
| 11. C2×C4×D97 | C4 | semidirect |
| 12. C2×C4×D97 | C4 | semidirect |
| 15. C22×C4×C97 | C4 | semidirect |
| 24. C2×#87604 | C2×C4 | semidirect |
| 37. C22×C97 | C42 | semidirect |
| 42. C2×D97 | C42 | semidirect |
| 48. C4×C97 | C22⋊C4 | semidirect |
| 50. Dic97 | C22⋊C4 | semidirect |
| 57. C97 | C4×C22⋊C4 | semidirect |
| 71. C22×C4 | #87604 | semidirect |
| 102. C22 | C4×#87604 | semidirect |
| 108. C4 | C22⋊#87604 | direct (N × H) |