Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1494 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 295 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 |
|---|---|---|
| 2. #14531456 | C2 | semidirect |
| 3. #14529198 | C2 | semidirect |
| 4. #14529067 | C2 | semidirect |
| 6. #99×Dic17 | C2 | semidirect |
| 14. C22×C4⋊Dic17 | C22 | semidirect |
| 21. #11762684 | C22 | semidirect |
| 22. #11762672 | C22 | semidirect |
| 23. C22⋊C4×Dic17 | C22 | semidirect |
| 24. #11762575 | C22 | semidirect |
| 27. C17×#458 | C4 | semidirect |
| 40. C17×#123 | C2×C4 | semidirect |
| 69. C17×#99 | C2×C4 | semidirect |
| 93. C22×C4×C17 | C22×C4 | semidirect |
| 112. C22⋊C4×C17 | C22×C4 | semidirect |
| 212. #458 | Dic17 | semidirect |
| 241. #123 | C2×Dic17 | semidirect |
| 271. #99 | C2×Dic17 | semidirect |
| 277. C17 | #21481 | semidirect |
| 310. C22×C4 | C22×Dic17 | semidirect |
| 325. C22⋊C4 | C22×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic17 | 2 |
| #14531456 | 2 |
| #14529198 | 2 |
| #14529067 | 2 |
| #14528732 | 2 |
| #99×Dic17 | 2 |
| C2×C17×#458 | 2 |
| #21481 | 17 |