Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #3633 |
| commutator, hypocenter | C17 | C2×C4×C32 |
| Frattini | C2×C4 | C22×#3633 |
| Fitting | C22×C8×C17 | C8 |
| socle, prime radical | C23×C17 | C2×C16 |
| cosocle | C2×#63216 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14545867 | C2 | direct (N × H) |
| 4. C2×#10587528 | C4 | semidirect |
| 19. #10587528 | C2×C4 | semidirect |
| 41. C2×Dic17 | C32 | semidirect |
| 56. Dic17 | C2×C32 | semidirect |
| 64. C2×C17 | C4×C32 | semidirect |
| 78. C17 | C2×C4×C32 | semidirect |
| 110. C2 | #14545867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587528 | 2 |
| #14545867 | 2 |
| C2×#11763695 | 2 |
| C2×C4×C32 | 17 |