Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
298 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 70 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 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C42×C17 |
| Frattini, cosocle | C2×#124 | C22×C17 |
| prime radical | C22×D4×C17 | C2×C4 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C17 ◁ C22×C4×C17 ◁ C2×C17×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C17×#355 | C4 | semidirect |
| 14. C17×#329 | C4 | semidirect |
| 70. #7487 | C17 | direct (N × H) |
| 126. #355 | C4×C17 | semidirect |
| 129. #329 | C4×C17 | semidirect |
| 157. C17 | #7487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#355 | 2 |
| C17×#1885 | 2 |
| C2×C17×#329 | 2 |
| #7487 | 17 |