Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. #22571334 | C2 | semidirect |
| 2. #22571131 | C2 | semidirect |
| 3. #22561182 | C2 | semidirect |
| 4. #22558769 | C2 | semidirect |
| 5. #22558769 | C2 | semidirect |
| 6. #22558054 | C2 | semidirect |
| 115. C2×C8×C67 | SD16 | semidirect |
| 203. C67 | #10221 | semidirect |
| 306. C2×C8 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571334 | 2 |
| #22571131 | 2 |
| #22561182 | 2 |
| #22558769 | 2 |
| #22558054 | 2 |
| C67×#3150 | 2 |
| #10221 | 67 |