Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22562094 | C2 | semidirect |
| 3. #22562084 | C2 | semidirect |
| 4. #22558398 | C2 | semidirect |
| 5. #22558395 | C2 | semidirect |
| 6. #22558344 | C2 | semidirect |
| 7. C67×#1426 | C2 | semidirect |
| 12. #16863235 | C4 | semidirect |
| 13. D2144 | C4 | semidirect |
| 25. Dic536 | C2×C4 | semidirect |
| 29. D1072 | C2×C4 | semidirect |
| 38. C32×C67 | C2×C4 | semidirect |
| 91. #1426 | D67 | semidirect |
| 95. C67 | #13658 | semidirect |
| 126. C32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562524 | 2 |
| #22562094 | 2 |
| #22562084 | 2 |
| #22558398 | 2 |
| #22558395 | 2 |
| #22558344 | 2 |
| C67×#1426 | 2 |
| #13658 | 67 |