Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #22571550 | C2 | semidirect |
| 5. #22558220 | C2 | semidirect |
| 6. #22558148 | C2 | semidirect |
| 7. C67×#1348 | C2 | semidirect |
| 136. C2×Dic67 | SD32 | semidirect |
| 181. #1348 | D67 | semidirect |
| 183. C67 | #12159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571550 | 2 |
| #22562140 | 2 |
| #22562137 | 2 |
| #22561521 | 2 |
| #22558220 | 2 |
| #22558148 | 2 |
| C67×#1348 | 2 |
| #12159 | 67 |