Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
430 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16863211 | C2 | semidirect |
| 5. C2×#16863199 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 7. C67×#1952 | C2 | semidirect |
| 186. #1952 | D67 | semidirect |
| 188. C67 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570703 | 2 |
| C2×#16863211 | 2 |
| C2×#16863202 | 2 |
| #22561919 | 2 |
| C2×#16863199 | 2 |
| #22558298 | 2 |
| C67×#1952 | 2 |
| #13412 | 67 |