Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22558967 | C2 | semidirect |
| 3. #22558964 | C2 | semidirect |
| 5. C67⋊#1309 | C2 | semidirect |
| 6. C67⋊#1309 | C2 | semidirect |
| 164. C67 | #8640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568921 | 2 |
| #22558967 | 2 |
| #22558964 | 2 |
| #22558944 | 2 |
| C67⋊#1309 | 2 |
| C67×#1560 | 2 |
| #8640 | 67 |