Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2127 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | #124 | C23×C17 |
| prime radical | C17×#3221 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#536 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#2133 | C2 | semidirect |
| 3. C17×#2129 | C2 | semidirect |
| 4. C17×#1414 | C2 | semidirect |
| 5. C17×#1406 | C2 | semidirect |
| 6. C17×#540 | C4 | semidirect |
| 9. C17×#492 | C4 | semidirect |
| 10. C17×#491 | C4 | semidirect |
| 16. C17×#433 | C4 | semidirect |
| 95. #13606 | C17 | direct (N × H) |
| 128. #2133 | C2×C17 | semidirect |
| 129. #2129 | C2×C17 | semidirect |
| 130. #1414 | C2×C17 | semidirect |
| 131. #1406 | C2×C17 | semidirect |
| 149. #540 | C4×C17 | semidirect |
| 152. #492 | C4×C17 | semidirect |
| 153. #491 | C4×C17 | semidirect |
| 159. #433 | C4×C17 | semidirect |
| 204. C17 | #13606 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3221 | 2 |
| C17×#2133 | 2 |
| C17×#2129 | 2 |
| C17×#1414 | 2 |
| C17×#1406 | 2 |
| #13606 | 17 |