Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4032 conjugacy classes of subgroups; only the 370 normal subgroups are shown.
This group has 4032 conjugacy classes of subgroups — too many to draw. Only its 370 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×#120 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| prime radical | C22×C17×H(5,𝔽2) | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C25×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×#458 | C2 | semidirect |
| 3. C17×#2405 | C2 | semidirect |
| 4. C17×#1790 | C2 | semidirect |
| 5. C17×#1781 | C2 | semidirect |
| 12. C2×C17×#123 | C22 | semidirect |
| 13. C22×C22⋊C4×C17 | C22 | semidirect |
| 15. C2×C17×#99 | C22 | semidirect |
| 17. C17×#386 | C22 | semidirect |
| 20. C17×#379 | C22 | semidirect |
| 43. C23×C4×C17 | C23 | semidirect |
| 44. C23×C4×C17 | C23 | semidirect |
| 53. C2×C22⋊C4×C17 | C23 | semidirect |
| 109. #32900 | C17 | direct (N × H) |
| 157. C2×#458 | C2×C17 | semidirect |
| 158. #2405 | C2×C17 | semidirect |
| 159. #1790 | C2×C17 | semidirect |
| 160. #1781 | C2×C17 | semidirect |
| 179. C22×C17 | #458 | semidirect |
| 192. C2×#123 | C22×C17 | semidirect |
| 193. C22×C22⋊C4 | C22×C17 | semidirect |
| 195. C2×#99 | C22×C17 | semidirect |
| 197. #386 | C22×C17 | semidirect |
| 200. #379 | C22×C17 | semidirect |
| 230. C23×C4 | C23×C17 | semidirect |
| 231. C23×C4 | C23×C17 | semidirect |
| 240. C2×C22⋊C4 | C23×C17 | semidirect |
| 243. C17 | #32900 | direct (N × H) |
| 361. C22 | C17×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C17×H(5,𝔽2) | 2 |
| C2×C17×#458 | 2 |
| C17×#2405 | 2 |
| C17×#1790 | 2 |
| C17×#1781 | 2 |
| #32900 | 17 |