Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊C4×D97 |
| commutator | C22×C97 | C22×C4 |
| Frattini | C23 | C22×D97 |
| Fitting | #99×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #99 | D97 |
| hypocenter | C97 | #410 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15690766 | C2 | semidirect |
| 3. #15690725 | C2 | semidirect |
| 4. #15690724 | C2 | semidirect |
| 5. #99×C97 | C2 | semidirect |
| 8. C2×Dic194 | C4 | semidirect |
| 9. C2×C22⋊D97 | C4 | semidirect |
| 11. C22×Dic97 | C4 | semidirect |
| 13. C2×C4×D97 | C4 | semidirect |
| 57. C97 | #410 | semidirect |
| 63. #99 | D97 | semidirect |