Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13093996 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#421 | C2 |
| socle | C2×C47 | #390 |
| hypercenter | #421 | D47 |
| hypocenter | C47 | #1976 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689159 | C2 | semidirect |
| 3. #15689139 | C2 | semidirect |
| 4. #15689097 | C2 | semidirect |
| 5. #15689096 | C2 | semidirect |
| 6. #15689081 | C2 | semidirect |
| 7. C47×#421 | C2 | semidirect |
| 13. C2×#10625337 | C4 | semidirect |
| 14. C2×#10625335 | C4 | semidirect |
| 15. C2×#10625336 | C4 | semidirect |
| 16. C2×#10625334 | C4 | semidirect |
| 136. #421 | D47 | semidirect |
| 140. C47 | #1976 | semidirect |