Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #595 |
| commutator, hypocenter | C17 | C2×C4×C32 |
| Frattini | C16 | C22×#595 |
| Fitting | C2×C17×C32 | C4 |
| socle | C22×C17 | C4×C16 |
| prime radical | C22×D17 | C2×C16 |
| cosocle | C16×D17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#595 | C2 | direct (N × H) |
| 7. #11763740 | C4 | semidirect |
| 9. C2×#10587467 | C4 | semidirect |
| 13. C2×#10587465 | C4 | semidirect |
| 14. C32×D17 | C4 | semidirect |
| 16. C2×C17×C32 | C4 | semidirect |
| 31. #10587467 | C2×C4 | semidirect |
| 32. C17×C32 | C2×C4 | semidirect |
| 33. #10587465 | C2×C4 | semidirect |
| 54. C2×#595 | C32 | direct (N × H) |
| 75. #595 | C2×C32 | direct (N × H) |
| 89. C2×C32 | #595 | direct (N × H) |
| 92. C2×C17 | C4×C32 | semidirect |
| 94. D17 | C4×C32 | semidirect |
| 112. C32 | C2×#595 | direct (N × H) |
| 113. C17 | C2×C4×C32 | semidirect |
| 157. C2 | C32×#595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763740 | 2 |
| C2×C16×#595 | 2 |
| C32×#595 | 2 |
| C2×C32×D17 | 2 |
| C2×C4×C32 | 17 |