Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1318 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #14529927 | C2 | semidirect |
| 4. #14529867 | C2 | semidirect |
| 5. #14529139 | C2 | semidirect |
| 6. #14529097 | C2 | semidirect |
| 7. #14528855 | C2 | semidirect |
| 8. C2×C17×#541 | C2 | semidirect |
| 13. C2×#10587506 | C22 | semidirect |
| 20. #11762571 | C22 | semidirect |
| 21. #11762564 | C22 | semidirect |
| 22. #11762564 | C22 | semidirect |
| 24. C2×C17×C4⋊Q8 | C22 | semidirect |
| 27. C2×C17×#125 | C22 | semidirect |
| 29. C2×C4×Q8×C17 | C22 | semidirect |
| 160. C2×#541 | D17 | semidirect |
| 192. C2×C4⋊Q8 | C2×D17 | semidirect |
| 195. C2×#125 | C2×D17 | semidirect |
| 197. C2×C4×Q8 | C2×D17 | semidirect |
| 258. C17 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762959 | 2 |
| #14531364 | 2 |
| #14529927 | 2 |
| #14529867 | 2 |
| #14529139 | 2 |
| #14529097 | 2 |
| #14528855 | 2 |
| C2×C17×#541 | 2 |
| #23942 | 17 |