Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #22558565 | C2 | semidirect |
| 5. C67⋊#1308 | C2 | semidirect |
| 6. #22558070 | C2 | semidirect |
| 7. C67×#1534 | C2 | semidirect |
| 155. #1534 | D67 | semidirect |
| 159. C67 | #9335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571399 | 2 |
| #22569279 | 2 |
| #22558915 | 2 |
| #22558565 | 2 |
| C67⋊#1308 | 2 |
| #22558070 | 2 |
| C67×#1534 | 2 |
| #9335 | 67 |