Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22561753 | C2 | semidirect |
| 4. #22558035 | C2 | semidirect |
| 5. #22558034 | C2 | semidirect |
| 7. C67×#2072 | C2 | semidirect |
| 195. #2072 | D67 | semidirect |
| 200. C67 | #7804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568153 | 2 |
| #22561753 | 2 |
| #22561613 | 2 |
| #22558035 | 2 |
| #22558034 | 2 |
| #22558029 | 2 |
| C67×#2072 | 2 |
| #7804 | 67 |