Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Fitting | C47×#407 | C2 |
| hypercenter | #407 | D47 |
| hypocenter | C47 | #2920 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689177 | C2 | semidirect |
| 3. #15689173 | C2 | semidirect |
| 4. #15689146 | C2 | semidirect |
| 6. M16×Dic47 | C2 | semidirect |
| 17. Dic47⋊C8 | C22 | semidirect |
| 19. #13093934 | C22 | semidirect |
| 20. C8×Dic47 | C22 | semidirect |
| 67. C2×Dic47 | M16 | semidirect |
| 100. C47 | #2920 | semidirect |