Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22571214 | C2 | semidirect |
| 3. #22570758 | C2 | semidirect |
| 4. #22559528 | C2 | semidirect |
| 5. #22558808 | C2 | semidirect |
| 6. C67×#1534 | C2 | semidirect |
| 15. #16863806 | C22 | semidirect |
| 17. #16863790 | C22 | semidirect |
| 18. #16863756 | C22 | semidirect |
| 24. #16863135 | C22 | semidirect |
| 27. #330×C67 | C22 | semidirect |
| 156. #1534 | D67 | semidirect |
| 158. C67 | #19006 | semidirect |
| 178. #330 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864144 | 2 |
| #22571214 | 2 |
| #22570758 | 2 |
| #22559528 | 2 |
| #22558808 | 2 |
| C67×#1534 | 2 |
| #19006 | 67 |