Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
350 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 2. C4⋊C16×D67 | C2 | semidirect |
| 3. #22558971 | C2 | semidirect |
| 4. #22558267 | C2 | semidirect |
| 5. #22558256 | C2 | semidirect |
| 6. #22558254 | C2 | semidirect |
| 7. C67×#1365 | C2 | semidirect |
| 140. #1365 | D67 | semidirect |
| 143. C67 | #11982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570789 | 2 |
| C4⋊C16×D67 | 2 |
| #22558971 | 2 |
| #22558267 | 2 |
| #22558256 | 2 |
| #22558254 | 2 |
| C67×#1365 | 2 |
| #11982 | 67 |