Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
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×#16863184 | C2 | semidirect |
| 3. C4×#14523958 | C2 | semidirect |
| 4. C67×#1800 | C2 | semidirect |
| 5. C23×D268 | C4 | semidirect |
| 12. #16863256 | C4 | semidirect |
| 13. #16863251 | C4 | semidirect |
| 39. #14523958 | D4 | semidirect |
| 193. C4×C67 | AΣL(1,𝔽16) | semidirect |
| 207. #1800 | D67 | semidirect |
| 209. C67 | #13221 | semidirect |
| 400. C4 | #16863184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563565 | 2 |
| C2×#16863184 | 2 |
| C4×#14523958 | 2 |
| C67×#1800 | 2 |
| #13221 | 67 |