Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 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 |
| 3. C2×#16863219 | C2 | semidirect |
| 6. #22558312 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 19. #16863181 | C4 | semidirect |
| 145. #1388 | D67 | semidirect |
| 147. C67 | #12933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568817 | 2 |
| C2×#16863220 | 2 |
| C2×#16863219 | 2 |
| #22561838 | 2 |
| #22560265 | 2 |
| #22558312 | 2 |
| C67×#1388 | 2 |
| #12933 | 67 |