Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22560997 | C2 | semidirect |
| 5. #22558302 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 7. C67×#2161 | C2 | semidirect |
| 17. #16863213 | C4 | semidirect |
| 18. #16863210 | C4 | semidirect |
| 143. #2161 | D67 | semidirect |
| 149. C67 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569125 | 2 |
| #22561959 | 2 |
| C2×#16863202 | 2 |
| #22560997 | 2 |
| #22558302 | 2 |
| #22558299 | 2 |
| C67×#2161 | 2 |
| #12942 | 67 |