Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15688984 |
| commutator | C23×C47 | C22×C4 |
| Frattini | C24 | C22×D47 |
| Fitting | C2×#99×C47 | C2 |
| socle | C2×C47 | #381 |
| hypercenter | C2×#99 | D47 |
| hypocenter | C47 | #1828 |
| LCS | G ▷ C23×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ C2×#99 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15688890 | C2 | semidirect |
| 4. #15688889 | C2 | semidirect |
| 8. #13093983 | C4 | semidirect |
| 9. C2×C22⋊Dic47 | C4 | semidirect |
| 96. C47 | #1828 | semidirect |