Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C43 | C2 |
| prime radical | #13063296 | C2 |
| hypercenter | #124 | D43 |
| hypocenter | C43 | #542 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063325 | C2 | semidirect |
| 2. #13063318 | C2 | semidirect |
| 3. #13063311 | C2 | semidirect |
| 4. #13063309 | C2 | semidirect |
| 5. #13063302 | C2 | semidirect |
| 6. #13063301 | C2 | semidirect |
| 8. Q8×Dic43 | C2 | semidirect |
| 9. D4×Dic43 | C2 | semidirect |
| 10. #13063282 | C2 | semidirect |
| 11. #124×C43 | C2 | semidirect |
| 74. C43 | #542 | semidirect |
| 78. #124 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063325 | 2 |
| #13063318 | 2 |
| #13063311 | 2 |
| #13063309 | 2 |
| #13063302 | 2 |
| #13063301 | 2 |
| #13063296 | 2 |
| Q8×Dic43 | 2 |
| D4×Dic43 | 2 |
| #13063282 | 2 |
| #124×C43 | 2 |
| #542 | 43 |