Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
212 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22562047 | C2 | semidirect |
| 3. #22558284 | C2 | semidirect |
| 4. #22558182 | C2 | semidirect |
| 5. #22558181 | C2 | semidirect |
| 6. #22558125 | C2 | semidirect |
| 7. C67×#2170 | C2 | semidirect |
| 25. #14523989 | C8 | semidirect |
| 26. #14523987 | C8 | semidirect |
| 27. #14523986 | C8 | semidirect |
| 28. #14523984 | C8 | semidirect |
| 105. #2170 | D67 | semidirect |
| 110. C67 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562088 | 2 |
| #22562047 | 2 |
| #22558284 | 2 |
| #22558182 | 2 |
| #22558181 | 2 |
| #22558125 | 2 |
| C67×#2170 | 2 |
| #12047 | 67 |