Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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 | #386 |
| hypercenter | #421 | D47 |
| hypocenter | C47 | #1906 |
| 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. #41×Dic47 | C2 | semidirect |
| 3. C2×#13093950 | C2 | semidirect |
| 4. #15689096 | C2 | semidirect |
| 5. #15688894 | C2 | semidirect |
| 6. #15688882 | C2 | semidirect |
| 7. C47×#421 | C2 | semidirect |
| 10. #13094054 | C4 | semidirect |
| 12. #13094049 | C4 | semidirect |
| 45. C2×D188 | C2×C4 | semidirect |
| 47. C2×Dic94 | C2×C4 | semidirect |
| 68. #10625329 | C2×C4 | semidirect |
| 132. #421 | D47 | semidirect |
| 137. C47 | #1906 | semidirect |