Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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 | C23×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Fitting | #123×C43 | C2 |
| hypercenter | #123 | D43 |
| hypocenter | C43 | #540 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063321 | C2 | semidirect |
| 2. #13063315 | C2 | semidirect |
| 3. #13063310 | C2 | semidirect |
| 4. #13063309 | C2 | semidirect |
| 5. #13063307 | C2 | semidirect |
| 6. #13063300 | C2 | semidirect |
| 7. #13063299 | C2 | semidirect |
| 8. #13063298 | C2 | semidirect |
| 9. #13063298 | C2 | semidirect |
| 10. #13063298 | C2 | semidirect |
| 11. #13063297 | C2 | semidirect |
| 12. C4×C22⋊D43 | C2 | semidirect |
| 13. (C22⋊D43)⋊C4 | C2 | semidirect |
| 14. #13063283 | C2 | semidirect |
| 15. #123×C43 | C2 | semidirect |
| 116. C43 | #540 | semidirect |
| 122. #123 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063321 | 2 |
| #13063315 | 2 |
| #13063310 | 2 |
| #13063309 | 2 |
| #13063307 | 2 |
| #13063300 | 2 |
| #13063299 | 2 |
| #13063298 | 2 |
| #13063297 | 2 |
| C4×C22⋊D43 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063283 | 2 |
| #123×C43 | 2 |
| #540 | 43 |