Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14527668 | C2 | semidirect |
| 3. #14526744 | C2 | semidirect |
| 4. #14526700 | C2 | semidirect |
| 5. C17×#1372 | C2 | semidirect |
| 44. C16×C17 | M16 | semidirect |
| 64. #1372 | D17 | semidirect |
| 104. C17 | #12086 | semidirect |
| 120. C16 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D272 | 2 |
| #14527668 | 2 |
| #14526744 | 2 |
| #14526700 | 2 |
| C17×#1372 | 2 |
| #12086 | 17 |