Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22560414 | C2 | semidirect |
| 5. #22558095 | C2 | semidirect |
| 6. #22558056 | C2 | semidirect |
| 7. C67×#1851 | C2 | semidirect |
| 22. #16863132 | C4 | semidirect |
| 23. #16863132 | C4 | semidirect |
| 24. #16863129 | C4 | semidirect |
| 25. #16863129 | C4 | semidirect |
| 221. #1851 | D67 | semidirect |
| 225. C67 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569254 | 2 |
| #22560511 | 2 |
| #22560414 | 2 |
| #22558698 | 2 |
| #22558095 | 2 |
| #22558056 | 2 |
| C67×#1851 | 2 |
| #8875 | 67 |