Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690784 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #131×C97 | C2 |
| socle | C2×C97 | #121 |
| hypercenter | #131 | D97 |
| hypocenter | C97 | #471 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690840 | C2 | semidirect |
| 3. C2×#13095500 | C2 | semidirect |
| 4. #15690746 | C2 | semidirect |
| 5. #15690728 | C2 | semidirect |
| 6. #15690726 | C2 | semidirect |
| 7. #131×C97 | C2 | semidirect |
| 51. C97 | #471 | semidirect |
| 56. #131 | D97 | semidirect |