Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22561878 | C2 | semidirect |
| 3. #22558379 | C2 | semidirect |
| 4. #22558371 | C2 | semidirect |
| 5. C67×#2128 | C2 | semidirect |
| 6. #16864001 | C4 | semidirect |
| 7. #16863786 | C4 | semidirect |
| 10. #16863750 | C4 | semidirect |
| 15. #16863457 | C4 | semidirect |
| 27. #14524040 | C2×C4 | semidirect |
| 28. #14524035 | C2×C4 | semidirect |
| 42. #14523954 | C2×C4 | semidirect |
| 43. C4×C67⋊C8 | C2×C4 | semidirect |
| 161. #2128 | D67 | semidirect |
| 165. C67 | #13609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571259 | 2 |
| #22561878 | 2 |
| #22558379 | 2 |
| #22558371 | 2 |
| C67×#2128 | 2 |
| #13609 | 67 |