Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
530 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 530 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 |
|---|---|---|
| 2. #22562847 | C2 | semidirect |
| 3. #22561127 | C2 | semidirect |
| 4. #22558718 | C2 | semidirect |
| 5. #22558651 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 11. #16863687 | C4 | semidirect |
| 12. #16863592 | C4 | semidirect |
| 199. #1285 | D67 | semidirect |
| 200. C67 | #9329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570301 | 2 |
| #22562847 | 2 |
| #22561127 | 2 |
| #22558718 | 2 |
| #22558651 | 2 |
| #22558101 | 2 |
| C67×#1285 | 2 |
| #9329 | 67 |