Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22558810 | C2 | semidirect |
| 5. #22558564 | C2 | semidirect |
| 6. #22558120 | C2 | semidirect |
| 7. C67×#1299 | C2 | semidirect |
| 192. #1299 | D67 | semidirect |
| 193. C67 | #9351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570032 | 2 |
| #22569224 | 2 |
| #22558810 | 2 |
| #22558644 | 2 |
| #22558564 | 2 |
| #22558120 | 2 |
| C67×#1299 | 2 |
| #9351 | 67 |