Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22562394 | C2 | semidirect |
| 3. #22562389 | C2 | semidirect |
| 4. #22558223 | C2 | semidirect |
| 5. #22558223 | C2 | semidirect |
| 6. #22558135 | C2 | semidirect |
| 7. C67×#2078 | C2 | semidirect |
| 20. C22⋊(C67⋊C16) | C22 | semidirect |
| 21. C22⋊(C67⋊C16) | C22 | semidirect |
| 22. C2×#107×C67 | C22 | semidirect |
| 26. #341×C67 | C22 | semidirect |
| 167. #2078 | D67 | semidirect |
| 171. C67 | #12284 | semidirect |
| 180. C2×#107 | C2×D67 | semidirect |
| 190. #341 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571074 | 2 |
| #22562394 | 2 |
| #22562389 | 2 |
| #22558223 | 2 |
| #22558135 | 2 |
| C67×#2078 | 2 |
| #12284 | 67 |