Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22563389 | C2 | semidirect |
| 3. #22558927 | C2 | semidirect |
| 6. #22558074 | C2 | semidirect |
| 7. C67×#1288 | C2 | semidirect |
| 11. #16863747 | C4 | semidirect |
| 12. #16863743 | C4 | semidirect |
| 157. #1288 | D67 | semidirect |
| 158. C67 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570603 | 2 |
| #22563389 | 2 |
| #22558927 | 2 |
| #22558757 | 2 |
| #22558755 | 2 |
| #22558074 | 2 |
| C67×#1288 | 2 |
| #9430 | 67 |