Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22561828 | C2 | semidirect |
| 3. #22558159 | C2 | semidirect |
| 4. #22558147 | C2 | semidirect |
| 5. C67×#1321 | C2 | semidirect |
| 141. #1321 | D67 | semidirect |
| 142. C67 | #11485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568917 | 2 |
| #22561828 | 2 |
| #22558159 | 2 |
| #22558147 | 2 |
| C67×#1321 | 2 |
| #11485 | 67 |