Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22570249 | C2 | semidirect |
| 4. #22561149 | C2 | semidirect |
| 5. #22558613 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 199. #1275 | D67 | semidirect |
| 200. C67 | #10035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570555 | 2 |
| #22570249 | 2 |
| #22570241 | 2 |
| #22561149 | 2 |
| #22558613 | 2 |
| #22558609 | 2 |
| C67×#1275 | 2 |
| #10035 | 67 |