Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
At least 6595 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has at least 6595 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72217282 |
| commutator, cosocle | #6499867 | C22×C3 |
| Frattini | C27 | C22×A4 |
| Fitting | #72216433 | C3 |
| hypercenter | C22 | #72215851 |
| hypocenter | #62817 | C3×D4 |
| LCS | G ▷ #6499867 ▷ #62817 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72216927 | C2 | semidirect |
| 2. #72216887 | C2 | semidirect |
| 3. #72216433 | C3 | semidirect |
| 4. #72216427 | C2×C3 | semidirect |
| 5. #72216292 | C2×C3 | semidirect |
| 6. #72209720 | C2 | semidirect |
| 8. #72209716 | C2×C3 | semidirect |
| 9. #11710730 | D4 | semidirect |
| 11. #6342371 | A4 | semidirect |
| 12. C28 | C2×A4 | semidirect |
| 13. #62817 | C3×D4 | semidirect |
| 15. #14679 | C2×A4 | semidirect |
| 19. C25 | B(4,𝔽2)⋊C3 | semidirect |
| 21. C23×C4 | B(4,𝔽2)⋊C3 | semidirect |