Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22561901 | C2 | semidirect |
| 3. #22561900 | C2 | semidirect |
| 4. #22561858 | C2 | semidirect |
| 5. #22560257 | C2 | semidirect |
| 6. #22560011 | C2 | semidirect |
| 7. C67×#2122 | C2 | semidirect |
| 8. C22×#11761613 | C4 | semidirect |
| 16. #16863432 | C4 | semidirect |
| 17. #16863401 | C4 | semidirect |
| 18. #16863400 | C4 | semidirect |
| 222. #2122 | D67 | semidirect |
| 225. C67 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569854 | 2 |
| #22561901 | 2 |
| #22561900 | 2 |
| #22561858 | 2 |
| #22560257 | 2 |
| #22560011 | 2 |
| C67×#2122 | 2 |
| #13234 | 67 |