Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. #22573311 | C2 | semidirect |
| 3. C2×#16863207 | C2 | semidirect |
| 4. #22561936 | C2 | semidirect |
| 5. #22560265 | C2 | semidirect |
| 6. #22558309 | C2 | semidirect |
| 7. C67×#1388 | C2 | semidirect |
| 15. #16863672 | C4 | semidirect |
| 16. #16863667 | C4 | semidirect |
| 184. #1388 | D67 | semidirect |
| 186. C67 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| #22569930 | 2 |
| C2×#16863207 | 2 |
| #22561936 | 2 |
| #22560265 | 2 |
| #22558309 | 2 |
| C67×#1388 | 2 |
| #13070 | 67 |