Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3650 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 3650 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#16863541 | C2 | semidirect |
| 2. C2×#16863535 | C2 | semidirect |
| 3. #22565933 | C2 | semidirect |
| 4. #22560149 | C2 | semidirect |
| 5. #22560144 | C2 | semidirect |
| 6. #22560121 | C2 | semidirect |
| 7. C22×2−1+4×C67 | C2 | semidirect |
| 55. C2×#41×C67 | D4 | semidirect |
| 62. C22×Q8×C67 | D4 | semidirect |
| 186. C22×2−1+4 | D67 | semidirect |
| 193. C67 | #32885 | semidirect |
| 223. C2×#41 | C22⋊D67 | semidirect |
| 230. C22×Q8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863541 | 2 |
| C2×#16863535 | 2 |
| #22565933 | 2 |
| #22560149 | 2 |
| #22560144 | 2 |
| #22560121 | 2 |
| C22×2−1+4×C67 | 2 |
| #32885 | 67 |