Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562495 | C2 | semidirect |
| 4. #22559728 | C2 | semidirect |
| 5. #22558262 | C2 | semidirect |
| 6. #22558192 | C2 | semidirect |
| 85. D8×C67 | Q16 | semidirect |
| 143. C67 | #12414 | semidirect |
| 205. D8 | Dic268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573165 | 2 |
| #22562495 | 2 |
| #22562356 | 2 |
| #22559728 | 2 |
| #22558262 | 2 |
| #22558192 | 2 |
| C67×#1333 | 2 |
| #12414 | 67 |