Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
542 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 2. #22561197 | C2 | semidirect |
| 4. #22558964 | C2 | semidirect |
| 5. #22558889 | C2 | semidirect |
| 6. #22558490 | C2 | semidirect |
| 69. #11761612 | SD16 | semidirect |
| 131. C67⋊C8 | #100 | semidirect |
| 161. C67 | #9793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863768 | 2 |
| #22561197 | 2 |
| #22561050 | 2 |
| #22558964 | 2 |
| #22558889 | 2 |
| #22558490 | 2 |
| C67×#1545 | 2 |
| #9793 | 67 |