Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
412 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #1555 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| prime radical | C17×#3151 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×M16×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#2165 | C2 | semidirect |
| 3. C17×#1359 | C2 | semidirect |
| 4. C17×#1357 | C2 | semidirect |
| 14. C17×#364 | C22 | semidirect |
| 70. #11992 | C17 | direct (N × H) |
| 98. #2165 | C2×C17 | semidirect |
| 99. #1359 | C2×C17 | semidirect |
| 100. #1357 | C2×C17 | semidirect |
| 125. #364 | C22×C17 | semidirect |
| 157. C17 | #11992 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3151 | 2 |
| C17×#2165 | 2 |
| C17×#1359 | 2 |
| C17×#1357 | 2 |
| #11992 | 17 |