Finite Group DatabasebetaFinite Group DatabasebetaOrder 6144.
Only the 97 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 97 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊#5464 | C23 |
| Frattini, socle | C22 | C22×#87588 |
| Fitting | #72237305 | D3 |
| LCS | G ▷ C22⋊#5464 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72261016 | C2 | semidirect |
| 2. #72260994 | C2 | semidirect |
| 3. #72260975 | C22 | semidirect |
| 4. #72260914 | C2 | semidirect |
| 5. #72237305 | D3 | semidirect |
| 6. #72235035 | C22 | semidirect |
| 7. #72235027 | C22 | semidirect |
| 8. C22⋊#5464 | C23 | semidirect |
| 9. #10586796 | C2×D3 | semidirect |
| 10. C22×#3549 | C2×D3 | semidirect |
| 11. #63040 | S4 | semidirect |
| 13. C2×#3549 | S4 | semidirect |
| 14. C22×H(3,𝔽4) | C22×D3 | semidirect |
| 18. #3549 | C2×S4 | semidirect |
| 19. #3549 | C2×S4 | semidirect |
| 20. C2×H(3,𝔽4) | C2×S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72261223 | 3 |
| #72261016 | 2 |
| #72260994 | 2 |
| #72260914 | 2 |
| C2×#11715691 | 4 |
| #72237389 | 4 |
| #72235037 | 4 |
| C2×#11715758 | 4 |