Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
190 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C17 | D4 |
| commutator | C4 | C4×C16×C17 |
| Frattini, cosocle | C22×C16 | C22×C17 |
| socle | C22×C17 | C4⋊C16 |
| prime radical | C23×C17 | M32 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C17 ◁ C22×C16×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C17×M64 | C4 | semidirect |
| 39. #7467 | C17 | direct (N × H) |
| 69. M64 | C4×C17 | semidirect |
| 89. C17 | #7467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×M64 | 2 |
| C2×C4×C16×C17 | 2 |
| #7467 | 17 |