Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
560 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22558935 | C2 | semidirect |
| 4. #22558811 | C2 | semidirect |
| 6. #22558102 | C2 | semidirect |
| 7. C67×#2660 | C2 | semidirect |
| 179. #2660 | D67 | semidirect |
| 184. C67 | #10091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571399 | 2 |
| #22570666 | 2 |
| #22558935 | 2 |
| #22558811 | 2 |
| #22558716 | 2 |
| #22558102 | 2 |
| C67×#2660 | 2 |
| #10091 | 67 |