Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #14539699 | C2 | semidirect |
| 2. #14537178 | C2 | semidirect |
| 3. #14529613 | C2 | semidirect |
| 4. #14527452 | C2 | semidirect |
| 5. #14527451 | C2 | semidirect |
| 6. #14526616 | C2 | semidirect |
| 7. C17×#3205 | C2 | semidirect |
| 38. C17×C4⋊Q8 | D4 | semidirect |
| 43. C17×#127 | D4 | semidirect |
| 63. C17×C4⋊C8 | D4 | semidirect |
| 72. C4⋊#3622 | D4 | semidirect |
| 125. C4×Dic17 | D8 | semidirect |
| 180. #3205 | D17 | semidirect |
| 249. C4⋊Q8 | C22⋊D17 | semidirect |
| 262. #127 | C22⋊D17 | semidirect |
| 275. C4⋊C8 | C22⋊D17 | semidirect |
| 283. C17 | #10280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14537178 | 2 |
| #14529613 | 2 |
| #14527452 | 2 |
| #14527451 | 2 |
| #14526616 | 2 |
| C17×#3205 | 2 |
| #10280 | 17 |