Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22561177 | C2 | semidirect |
| 4. C2×#16863137 | C2 | semidirect |
| 6. #22558090 | C2 | semidirect |
| 7. C67×#1836 | C2 | semidirect |
| 210. #1836 | D67 | semidirect |
| 214. C67 | #10426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568261 | 2 |
| #22561177 | 2 |
| #22561023 | 2 |
| C2×#16863137 | 2 |
| C2×#16863135 | 2 |
| #22558090 | 2 |
| C67×#1836 | 2 |
| #10426 | 67 |