Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D43 |
| commutator, cosocle | C4×C43 | C24 |
| Frattini | C4 | C23×D43 |
| Fitting | #135×C43 | C2 |
| socle | C2×C43 | C22×D4 |
| hypercenter | #135 | D43 |
| hypocenter | C43 | #578 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063372 | C2 | semidirect |
| 2. #13063355 | C2 | semidirect |
| 3. #13063354 | C2 | semidirect |
| 4. #13063344 | C2 | semidirect |
| 5. C2×Dic172 | C2 | semidirect |
| 6. Q16×D43 | C2 | semidirect |
| 7. #13063331 | C2 | semidirect |
| 8. #135×C43 | C2 | semidirect |
| 60. C43 | #578 | semidirect |
| 65. #135 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063372 | 2 |
| #13063355 | 2 |
| #13063354 | 2 |
| #13063344 | 2 |
| C2×Dic172 | 2 |
| Q16×D43 | 2 |
| #13063331 | 2 |
| #135×C43 | 2 |
| #578 | 43 |