Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
844 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 103 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×#11762597 | C2 | semidirect |
| 3. C4×#10587505 | C2 | semidirect |
| 4. C17×#1800 | C2 | semidirect |
| 5. C23×D68 | C4 | semidirect |
| 12. #11762669 | C4 | semidirect |
| 13. #11762664 | C4 | semidirect |
| 52. #10587505 | D4 | semidirect |
| 166. #1800 | D17 | semidirect |
| 198. C4×C17 | AΣL(1,𝔽16) | semidirect |
| 259. C17 | #13221 | semidirect |
| 400. C4 | #11762597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14532140 | 2 |
| C2×#11762597 | 2 |
| C4×#10587505 | 2 |
| C17×#1800 | 2 |
| #13221 | 17 |