Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
740 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 101 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. #14539722 | C2 | semidirect |
| 2. #14538577 | C2 | semidirect |
| 4. #14527451 | C2 | semidirect |
| 5. #14527176 | C2 | semidirect |
| 6. #14526687 | C2 | semidirect |
| 7. C17×#1503 | C2 | semidirect |
| 37. C17×C4⋊Q8 | D4 | semidirect |
| 38. C17×C4⋊Q8 | D4 | semidirect |
| 75. C4⋊#3622 | D4 | semidirect |
| 76. C4⋊#3622 | D4 | semidirect |
| 107. C2×D68 | SD16 | semidirect |
| 192. #1503 | D17 | semidirect |
| 260. C4⋊Q8 | D68 | semidirect |
| 261. C4⋊Q8 | D68 | semidirect |
| 299. C17 | #10246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539722 | 2 |
| #14538577 | 2 |
| #14533726 | 2 |
| #14527451 | 2 |
| #14527176 | 2 |
| #14526687 | 2 |
| C17×#1503 | 2 |
| #10246 | 17 |