Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14539336 | C2 | semidirect |
| 3. #14538607 | C2 | semidirect |
| 4. #14534729 | C2 | semidirect |
| 5. #14529995 | C2 | semidirect |
| 6. #14529764 | C2 | semidirect |
| 7. #14528996 | C2 | semidirect |
| 8. #14528597 | C2 | semidirect |
| 9. C17×#1965 | C2 | semidirect |
| 114. M16×C17 | #41 | semidirect |
| 183. #1965 | D17 | semidirect |
| 288. C17 | #25690 | semidirect |
| 314. M16 | #63254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14542658 | 2 |
| #14539336 | 2 |
| #14538607 | 2 |
| #14534729 | 2 |
| #14529995 | 2 |
| #14529764 | 2 |
| #14528996 | 2 |
| #14528597 | 2 |
| C17×#1965 | 2 |
| #25690 | 17 |