Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C22×D4×C43 | C2 |
| hypercenter | C22×D4 | D43 |
| hypocenter | C43 | #534 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D43 | C2 | semidirect |
| 2. #13063308 | C2 | semidirect |
| 3. #13063306 | C2 | semidirect |
| 4. #13063297 | C2 | semidirect |
| 5. #13063294 | C2 | semidirect |
| 6. #13063293 | C2 | semidirect |
| 7. C2×C22⋊Dic43 | C2 | semidirect |
| 8. C22×D4×C43 | C2 | semidirect |
| 10. C24×C43 | C22 | semidirect |
| 11. C23×D43 | C22 | semidirect |
| 14. C2×D4×C43 | C22 | semidirect |
| 15. C22×C4×C43 | C22 | semidirect |
| 18. C2×C22⋊D43 | C22 | semidirect |
| 19. C2×C22⋊D43 | C22 | semidirect |
| 20. C22×Dic43 | C22 | semidirect |
| 21. C22×Dic43 | C22 | semidirect |
| 22. C22⋊Dic43 | C22 | semidirect |
| 23. C22⋊Dic43 | C22 | semidirect |
| 24. C22⋊Dic43 | C22 | semidirect |
| 25. (C2×D43)⋊C4 | C22 | semidirect |
| 26. Dic43⋊C4 | C22 | semidirect |
| 30. C23×C43 | D4 | semidirect |
| 74. C43 | #534 | semidirect |
| 76. C22×D4 | D43 | semidirect |
| 85. C24 | C2×D43 | semidirect |
| 92. C2×D4 | C2×D43 | semidirect |
| 95. C22×C4 | C2×D43 | semidirect |
| 107. C23 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D43 | 2 |
| #13063308 | 2 |
| #13063306 | 2 |
| #13063297 | 2 |
| #13063294 | 2 |
| #13063293 | 2 |
| C2×C22⋊Dic43 | 2 |
| C22×D4×C43 | 2 |
| #534 | 43 |