Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
406 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#2162 | C2 | semidirect |
| 3. C17×#1568 | C2 | semidirect |
| 4. C17×#1360 | C2 | semidirect |
| 15. C17×C4⋊C16 | C22 | semidirect |
| 19. C17×#334 | C22 | semidirect |
| 83. #11957 | C17 | direct (N × H) |
| 113. #2162 | C2×C17 | semidirect |
| 114. #1568 | C2×C17 | semidirect |
| 115. #1360 | C2×C17 | semidirect |
| 142. C4⋊C16 | C22×C17 | semidirect |
| 146. #334 | C22×C17 | semidirect |
| 180. C17 | #11957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#495 | 2 |
| C17×#2162 | 2 |
| C17×#1568 | 2 |
| C17×#1360 | 2 |
| #11957 | 17 |