Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
632 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14538788 | C2 | semidirect |
| 2. #14538577 | C2 | semidirect |
| 4. #14527210 | C2 | semidirect |
| 5. #14527174 | C2 | semidirect |
| 6. #14526642 | C2 | semidirect |
| 7. C17×#1518 | C2 | semidirect |
| 38. C17×C4⋊Q8 | D4 | semidirect |
| 39. C17×C4⋊Q8 | D4 | semidirect |
| 82. C4⋊#3622 | D4 | semidirect |
| 83. C4×#3622 | D4 | semidirect |
| 105. C2×D68 | SD16 | semidirect |
| 204. #1518 | D17 | semidirect |
| 277. C4⋊Q8 | D68 | semidirect |
| 278. C4⋊Q8 | D68 | semidirect |
| 321. C17 | #10000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538788 | 2 |
| #14538577 | 2 |
| #14533686 | 2 |
| #14527210 | 2 |
| #14527174 | 2 |
| #14526642 | 2 |
| C17×#1518 | 2 |
| #10000 | 17 |