Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16863758 | C2 | semidirect |
| 3. #22559530 | C2 | direct (N × H) |
| 4. C2×#16863138 | C2 | semidirect |
| 5. C2×#16863135 | C2 | semidirect |
| 6. C2×#491×C67 | C2 | semidirect |
| 15. #16863758 | C22 | semidirect |
| 19. #16863138 | C22 | semidirect |
| 20. #16863135 | C22 | semidirect |
| 24. #491×C67 | C22 | semidirect |
| 145. C2×C67 | #1662 | semidirect |
| 150. C2×#491 | D67 | semidirect |
| 155. C67 | C2×#1662 | semidirect |
| 166. #491 | C2×D67 | semidirect |
| 294. C2 | #22559530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864144 | 2 |
| C2×#16863758 | 2 |
| #22559530 | 2 |
| C2×#16863138 | 2 |
| C2×#16863135 | 2 |
| C2×#491×C67 | 2 |
| C2×#1662 | 67 |