Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16863225 | C2 | semidirect |
| 5. #22561000 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 19. #16863202 | C4 | semidirect |
| 146. #1388 | D67 | semidirect |
| 148. C67 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569125 | 2 |
| C2×#16863225 | 2 |
| #22561938 | 2 |
| C2×#16863202 | 2 |
| #22561000 | 2 |
| #22558299 | 2 |
| C67×#1388 | 2 |
| #12947 | 67 |