Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4122 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 4122 conjugacy classes of subgroups — too many to draw. Only its 555 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10587505 | C2 | semidirect |
| 2. #14531362 | C2 | semidirect |
| 3. #14528732 | C2 | semidirect |
| 5. C22×C22⋊Dic17 | C22 | semidirect |
| 6. C22×C22⋊Dic17 | C22 | semidirect |
| 8. C2×#10587505 | C22 | semidirect |
| 10. #11762689 | C22 | semidirect |
| 15. C2×C17×H(5,𝔽2) | C4 | semidirect |
| 26. C17×H(5,𝔽2) | C2×C4 | semidirect |
| 47. C23×Dic17 | C23 | semidirect |
| 53. C2×C22⋊Dic17 | C23 | semidirect |
| 64. C24×C17 | C22⋊C4 | semidirect |
| 89. C2×D4×C17 | C22⋊C4 | semidirect |
| 97. C22×C4×C17 | C22⋊C4 | semidirect |
| 183. C2×H(5,𝔽2) | Dic17 | semidirect |
| 209. H(5,𝔽2) | C2×Dic17 | semidirect |
| 239. C17 | #20609 | semidirect |
| 248. C24 | C22⋊Dic17 | semidirect |
| 273. C2×D4 | C22⋊Dic17 | semidirect |
| 286. C22×C4 | C22⋊Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587505 | 2 |
| #14531362 | 2 |
| #14528732 | 2 |
| C22×C17×H(5,𝔽2) | 2 |
| #20609 | 17 |