Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
126 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | D16 |
| commutator | C16 | C2×C8×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle, prime radical | C22×C17 | #357 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C17×Q32 | C8 | semidirect |
| 35. #7384 | C17 | direct (N × H) |
| 71. Q32 | C8×C17 | semidirect |
| 79. C17 | #7384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C17×Q32 | 2 |
| C4×C17×C32 | 2 |
| C17×#1371 | 2 |
| #7384 | 17 |