Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 3. #14527453 | C2 | semidirect |
| 4. #14527283 | C2 | semidirect |
| 5. #14527175 | C2 | semidirect |
| 6. #14526685 | C2 | semidirect |
| 7. C17×#3077 | C2 | semidirect |
| 38. C17×C4⋊Q8 | D4 | semidirect |
| 39. C17×C4⋊Q8 | D4 | semidirect |
| 67. C17×C4⋊C8 | D4 | semidirect |
| 75. C4⋊#3622 | D4 | semidirect |
| 87. C2×D4×C17 | SD16 | semidirect |
| 189. #3077 | D17 | semidirect |
| 260. C4⋊Q8 | C22⋊D17 | semidirect |
| 261. C4⋊Q8 | C22⋊D17 | semidirect |
| 290. C4⋊C8 | C22⋊D17 | semidirect |
| 299. C17 | #10246 | semidirect |
| 324. C2×D4 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539722 | 2 |
| #14533730 | 2 |
| #14527453 | 2 |
| #14527283 | 2 |
| #14527175 | 2 |
| #14526685 | 2 |
| C17×#3077 | 2 |
| #10246 | 17 |