Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
566 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3109 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#3234 | C2 | semidirect |
| 3. C17×#2562 | C2 | semidirect |
| 4. C17×#1980 | C2 | semidirect |
| 5. C17×#1528 | C2 | semidirect |
| 6. C17×#1490 | C2 | semidirect |
| 7. C17×#1285 | C2 | semidirect |
| 136. #10005 | C17 | direct (N × H) |
| 184. #3234 | C2×C17 | semidirect |
| 186. #2562 | C2×C17 | semidirect |
| 187. #1980 | C2×C17 | semidirect |
| 188. #1528 | C2×C17 | semidirect |
| 189. #1490 | C2×C17 | semidirect |
| 190. #1285 | C2×C17 | semidirect |
| 299. C17 | #10005 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3234 | 2 |
| C17×#3109 | 2 |
| C17×#2562 | 2 |
| C17×#1980 | 2 |
| C17×#1528 | 2 |
| C17×#1490 | 2 |
| C17×#1285 | 2 |
| #10005 | 17 |