Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
270 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 216 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×C4×C8 | #595 |
| commutator, hypocenter | C17 | C2×C4×C32 |
| Frattini | C2×C8 | C22×#595 |
| Fitting | C2×C4×C8×C17 | C4 |
| socle, prime radical | C23×C17 | C2×C16 |
| cosocle | C2×#63214 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#10587467 | C2 | direct (N × H) |
| 4. C2×#10587467 | C4 | direct (N × H) |
| 21. #10587467 | C2×C4 | direct (N × H) |
| 37. C2×C4×C17 | C32 | semidirect |
| 54. C4×C17 | C2×C32 | semidirect |
| 64. C2×C17 | C4×C32 | semidirect |
| 78. C17 | C2×C4×C32 | semidirect |
| 93. C2×C4 | #10587467 | direct (N × H) |
| 107. C4 | C2×#10587467 | direct (N × H) |
| 110. C2 | C4×#10587467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587467 | 2 |
| C4×#10587467 | 2 |
| C2×C4×#63214 | 2 |
| C2×C4×C32 | 17 |