Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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×#380 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #380 | D47 |
| hypocenter | C47 | #2347 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689019 | C2 | semidirect |
| 4. #15688990 | C2 | semidirect |
| 5. C4⋊C4×Dic47 | C2 | semidirect |
| 6. #15688974 | C2 | semidirect |
| 9. #13093983 | C4 | semidirect |
| 103. C47 | #2347 | semidirect |