Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13093999 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#427 | C2 |
| socle | C2×C47 | #390 |
| hypercenter | #427 | D47 |
| hypocenter | C47 | #1976 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689141 | C2 | semidirect |
| 3. #15689096 | C2 | semidirect |
| 4. #15689078 | C2 | semidirect |
| 5. C47×#427 | C2 | semidirect |
| 11. C2×Dic188 | C4 | semidirect |
| 12. C2×#10625325 | C4 | semidirect |
| 13. C2×D376 | C4 | semidirect |
| 98. #427 | D47 | semidirect |
| 102. C47 | #1976 | semidirect |