Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 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×#16863224 | C2 | semidirect |
| 5. #22560994 | C2 | semidirect |
| 6. #22558318 | C2 | semidirect |
| 7. C67×#1379 | C2 | semidirect |
| 19. #16863204 | C4 | semidirect |
| 43. #14523979 | C2×C4 | semidirect |
| 60. C2×C16×C67 | C2×C4 | semidirect |
| 166. #1379 | D67 | semidirect |
| 167. C67 | #12946 | semidirect |
| 210. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569086 | 2 |
| C2×#16863224 | 2 |
| C2×#16863204 | 2 |
| #22561922 | 2 |
| #22560994 | 2 |
| #22558318 | 2 |
| C67×#1379 | 2 |
| #12946 | 67 |