Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D43 |
| commutator, socle | C22×C43 | C22×C4 |
| Fitting | #97×C43 | C2 |
| prime radical | C2×D172 | C4 |
| cosocle | C2×C4×C43 | C23 |
| hypercenter | #97 | D43 |
| hypocenter | C43 | #435 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10621872 | C2 | semidirect |
| 2. C2×C8×D43 | C2 | semidirect |
| 4. C4⋊(C43⋊C8) | C2 | semidirect |
| 5. (C2×D43)⋊C8 | C2 | semidirect |
| 6. (C2×D43)⋊C8 | C2 | semidirect |
| 7. #97×C43 | C2 | semidirect |
| 34. C8×C43 | D4 | semidirect |
| 43. C2×D43 | M16 | semidirect |
| 56. C43 | #435 | semidirect |
| 63. #97 | D43 | semidirect |
| 92. C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621872 | 2 |
| C2×C8×D43 | 2 |
| C4×D172 | 2 |
| C4⋊(C43⋊C8) | 2 |
| (C2×D43)⋊C8 | 2 |
| #97×C43 | 2 |
| #435 | 43 |