Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Frattini | C22 | C23×D43 |
| Fitting | #117×C43 | C2 |
| hypercenter | #117 | D43 |
| hypocenter | C43 | #525 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10621898 | C2 | semidirect |
| 2. C22×C4×D43 | C2 | semidirect |
| 3. #13063309 | C2 | semidirect |
| 4. #13063305 | C2 | semidirect |
| 5. #13063300 | C2 | semidirect |
| 6. #13063295 | C2 | semidirect |
| 7. C4×D172 | C2 | semidirect |
| 8. #117×C43 | C2 | semidirect |
| 15. C2×D172 | C22 | semidirect |
| 19. C2×C4×D43 | C22 | semidirect |
| 20. C2×Dic86 | C22 | semidirect |
| 21. C4⋊C4×C43 | C22 | semidirect |
| 23. C42×C43 | C22 | semidirect |
| 25. (C2×D43)⋊C4 | C22 | semidirect |
| 26. C4⋊Dic43 | C22 | semidirect |
| 32. C2×C4×C43 | D4 | semidirect |
| 54. C2×D43 | #41 | semidirect |
| 66. C43 | #525 | semidirect |
| 74. #117 | D43 | semidirect |
| 88. C4⋊C4 | C2×D43 | semidirect |
| 92. C42 | C2×D43 | semidirect |
| 108. C2×C4 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| C22×C4×D43 | 2 |
| #13063309 | 2 |
| #13063305 | 2 |
| #13063300 | 2 |
| #13063295 | 2 |
| C4×D172 | 2 |
| #117×C43 | 2 |
| #525 | 43 |