Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D47 |
| commutator | C22×C47 | C22×C8 |
| Fitting | C47×#336 | C2 |
| socle | C23×C47 | C22×C4 |
| hypercenter | #336 | D47 |
| hypocenter | C47 | #1869 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C8×D47 | C2 | semidirect |
| 3. C2×(C2×D47)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D47)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D47)⋊C8 | C2 | semidirect |
| 6. #15688878 | C2 | semidirect |
| 7. C47×#336 | C2 | semidirect |
| 36. C2×D188 | C8 | semidirect |
| 54. C2×C8×C47 | D4 | semidirect |
| 65. C2×C47⋊C8 | D4 | semidirect |
| 80. C22×D47 | C2×C8 | semidirect |
| 87. C2×C4×C47 | C2×C8 | semidirect |
| 133. C2×D47 | C22⋊C8 | semidirect |
| 158. #336 | D47 | semidirect |
| 159. C47 | #1869 | semidirect |
| 213. C2×C8 | D188 | semidirect |
| 254. C2×C4 | C8×D47 | semidirect |