Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 2. C2×#11762856 | C2 | semidirect |
| 3. #14530513 | C2 | semidirect |
| 4. #14530511 | C2 | semidirect |
| 5. C2×#11762590 | C2 | semidirect |
| 6. #14526900 | C2 | semidirect |
| 7. C17×#1389 | C2 | semidirect |
| 60. C17×#108 | D4 | semidirect |
| 65. #10587490 | D4 | semidirect |
| 168. #1389 | D17 | semidirect |
| 250. #108 | D68 | semidirect |
| 255. C17 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538394 | 2 |
| C2×#11762856 | 2 |
| #14530513 | 2 |
| #14530511 | 2 |
| C2×#11762590 | 2 |
| #14526900 | 2 |
| C17×#1389 | 2 |
| #12998 | 17 |