Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14531096 | C2 | semidirect |
| 2. #14531034 | C2 | semidirect |
| 3. #14526982 | C2 | semidirect |
| 4. #14526973 | C2 | semidirect |
| 5. C17×#2178 | C2 | semidirect |
| 22. C17×Q32 | D4 | semidirect |
| 24. C17×D16 | D4 | semidirect |
| 71. #2178 | D17 | semidirect |
| 102. Q32 | D68 | semidirect |
| 107. D16 | D68 | semidirect |
| 114. C17 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531096 | 2 |
| #14531034 | 2 |
| #14526982 | 2 |
| #14526973 | 2 |
| C17×#2178 | 2 |
| #13692 | 17 |