Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16863221 | C2 | semidirect |
| 5. #22560995 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 7. C67×#1387 | C2 | semidirect |
| 19. #16863202 | C4 | semidirect |
| 44. C2×C67⋊C16 | C2×C4 | semidirect |
| 60. #108×C67 | C2×C4 | semidirect |
| 165. #1387 | D67 | semidirect |
| 167. C67 | #12945 | semidirect |
| 212. #108 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569083 | 2 |
| C2×#16863221 | 2 |
| C2×#16863202 | 2 |
| #22561922 | 2 |
| #22560995 | 2 |
| #22558299 | 2 |
| C67×#1387 | 2 |
| #12945 | 67 |