Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C4×D4×C43 | C2 |
| hypercenter | C4×D4 | D43 |
| hypocenter | C43 | #547 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10621898 | C2 | semidirect |
| 2. #13063325 | C2 | semidirect |
| 3. #13063307 | C2 | semidirect |
| 4. #13063304 | C2 | semidirect |
| 5. #13063296 | C2 | semidirect |
| 6. C4×D172 | C2 | semidirect |
| 7. C4⋊C4×D43 | C2 | semidirect |
| 8. C4×D4×C43 | C2 | semidirect |
| 37. D172 | D4 | semidirect |
| 51. C4×C43 | #41 | semidirect |
| 60. C43 | #547 | semidirect |
| 67. C4×D4 | D43 | semidirect |
| 112. C4 | #10621898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063325 | 2 |
| #13063307 | 2 |
| #13063304 | 2 |
| #13063296 | 2 |
| C4×D172 | 2 |
| C4⋊C4×D43 | 2 |
| C4×D4×C43 | 2 |
| #547 | 43 |