Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22562932 | C2 | semidirect |
| 3. #22561042 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558067 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1517 | C2 | semidirect |
| 10. #16863772 | C4 | semidirect |
| 11. #16863744 | C4 | semidirect |
| 51. C4×C67⋊C8 | C2×C4 | semidirect |
| 55. C4⋊Q8×C67 | C2×C4 | semidirect |
| 56. #127×C67 | C2×C4 | semidirect |
| 98. C4×Dic67 | D8 | semidirect |
| 216. #1517 | D67 | semidirect |
| 219. C67 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D67 | semidirect |
| 251. #127 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22562932 | 2 |
| #22561042 | 2 |
| #22558876 | 2 |
| #22558067 | 2 |
| #22558037 | 2 |
| C67×#1517 | 2 |
| #9299 | 67 |