Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
272 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#340 | C2 |
| socle | C23×C47 | C2×D4 |
| hypercenter | #340 | D47 |
| hypocenter | C47 | #1776 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #13093957 | C4 | semidirect |
| 15. #13093955 | C4 | semidirect |
| 16. #13093934 | C4 | semidirect |
| 73. C47⋊C8 | C42 | semidirect |
| 106. C47 | #1776 | semidirect |