Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 122. #9995 | C17 | direct (N × H) |
| 259. C17 | #9995 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3195 | 2 |
| C2×C17×#484 | 2 |
| C2×C17×#483 | 2 |
| C17×#1821 | 2 |
| C17×#1472 | 2 |
| C17×#1298 | 2 |
| #9995 | 17 |