Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
170 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D97 |
| commutator | C22×C97 | C22×C4 |
| Fitting | C2×C42×C97 | C2 |
| socle | C23×C97 | C23 |
| hypercenter | C2×C42 | D97 |
| hypocenter | C97 | #389 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C4⋊Dic97 | C4 | semidirect |
| 40. C4×C97 | C4⋊C4 | semidirect |
| 50. C97 | #389 | semidirect |
| 93. C4 | #13095490 | semidirect |