Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 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 |
|---|---|---|
| 3. C2×#16863211 | C2 | semidirect |
| 4. #22561930 | C2 | semidirect |
| 6. #22558323 | C2 | semidirect |
| 7. C67×#1385 | C2 | semidirect |
| 16. #16863672 | C4 | semidirect |
| 168. #1385 | D67 | semidirect |
| 169. C67 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| C2×#16863672 | 2 |
| C2×#16863211 | 2 |
| #22561930 | 2 |
| #22560264 | 2 |
| #22558323 | 2 |
| C67×#1385 | 2 |
| #13069 | 67 |