Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
448 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22569284 | C2 | semidirect |
| 3. #22558821 | C2 | semidirect |
| 4. #22558820 | C2 | semidirect |
| 5. #22558072 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#1496 | C2 | semidirect |
| 180. #1496 | D67 | semidirect |
| 183. C67 | #9283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571138 | 2 |
| #22569284 | 2 |
| #22558821 | 2 |
| #22558820 | 2 |
| #22558072 | 2 |
| #22558039 | 2 |
| C67×#1496 | 2 |
| #9283 | 67 |