Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16863220 | C2 | semidirect |
| 5. #22558315 | C2 | semidirect |
| 6. #22558310 | C2 | semidirect |
| 7. C67×#2155 | C2 | semidirect |
| 19. #16863181 | C4 | semidirect |
| 43. C2×C67⋊C16 | C2×C4 | semidirect |
| 55. M32×C67 | C2×C4 | semidirect |
| 154. #2155 | D67 | semidirect |
| 160. C67 | #12934 | semidirect |
| 200. M32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568801 | 2 |
| C2×#16863220 | 2 |
| #22561838 | 2 |
| #22560264 | 2 |
| #22558315 | 2 |
| #22558310 | 2 |
| C67×#2155 | 2 |
| #12934 | 67 |