Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22570947 | C2 | semidirect |
| 2. #22562423 | C2 | semidirect |
| 3. #22562380 | C2 | semidirect |
| 4. #22562285 | C2 | semidirect |
| 5. #22562155 | C2 | semidirect |
| 6. #22562107 | C2 | semidirect |
| 7. #22562021 | C2 | semidirect |
| 8. C67×#2956 | C2 | semidirect |
| 11. #16863794 | C22 | semidirect |
| 12. #16863773 | C22 | semidirect |
| 17. #16863509 | C22 | semidirect |
| 18. #16863220 | C22 | semidirect |
| 19. #16863217 | C22 | semidirect |
| 20. #16863208 | C22 | semidirect |
| 23. #16863174 | C22 | semidirect |
| 96. Q16×C67 | #41 | semidirect |
| 100. D8×C67 | #41 | semidirect |
| 171. #2956 | D67 | semidirect |
| 178. C67 | #33688 | semidirect |
| 259. Q16 | #11761628 | semidirect |
| 265. D8 | #11761628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570947 | 2 |
| #22562423 | 2 |
| #22562380 | 2 |
| #22562285 | 2 |
| #22562155 | 2 |
| #22562107 | 2 |
| #22562021 | 2 |
| C67×#2956 | 2 |
| #33688 | 67 |