Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. C2×#16863221 | C2 | semidirect |
| 4. #22558287 | C2 | semidirect |
| 5. C67×#1845 | C2 | semidirect |
| 120. #1845 | D67 | semidirect |
| 122. C67 | #13526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863221 | 2 |
| C2×#16863196 | 2 |
| #22561075 | 2 |
| #22558287 | 2 |
| C67×#1845 | 2 |
| #13526 | 67 |