Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22569060 | C2 | semidirect |
| 3. #22562084 | C2 | semidirect |
| 4. #22562055 | C2 | semidirect |
| 5. #22561924 | C2 | semidirect |
| 6. #22561805 | C2 | semidirect |
| 7. C67×#2158 | C2 | semidirect |
| 10. C2×D1072 | C4 | semidirect |
| 15. #16863478 | C22 | semidirect |
| 18. #16863196 | C22 | semidirect |
| 19. #16863171 | C22 | semidirect |
| 20. C16×Dic67 | C22 | semidirect |
| 23. #367×C67 | C22 | semidirect |
| 24. #366×C67 | C22 | semidirect |
| 28. C2×D536 | C2×C4 | semidirect |
| 35. D1072 | C2×C4 | semidirect |
| 36. D1072 | C2×C4 | semidirect |
| 44. C2×C16×C67 | C2×C4 | semidirect |
| 113. #2158 | D67 | semidirect |
| 116. C67 | #33456 | semidirect |
| 129. #367 | C2×D67 | semidirect |
| 130. #366 | C2×D67 | semidirect |
| 150. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| #22569060 | 2 |
| #22562084 | 2 |
| #22562055 | 2 |
| #22561924 | 2 |
| #22561805 | 2 |
| C67×#2158 | 2 |
| #33456 | 67 |