Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C47×#382 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #382 | D47 |
| hypocenter | C47 | #2283 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15688990 | C2 | semidirect |
| 3. #15688989 | C2 | semidirect |
| 6. C4⋊C4×Dic47 | C2 | semidirect |
| 8. #15688968 | C2 | semidirect |
| 9. C47×#382 | C2 | semidirect |
| 19. C42×D47 | C4 | semidirect |
| 109. #382 | D47 | semidirect |
| 115. C47 | #2283 | semidirect |