Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
332 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C16×Dic67 | C2 | semidirect |
| 5. #22560955 | C2 | semidirect |
| 6. #22558306 | C2 | semidirect |
| 7. C67×#1381 | C2 | semidirect |
| 16. #16863201 | C4 | semidirect |
| 17. #16863198 | C4 | semidirect |
| 144. #1381 | D67 | semidirect |
| 145. C67 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863202 | 2 |
| #22561917 | 2 |
| C2×C16×Dic67 | 2 |
| #22561095 | 2 |
| #22560955 | 2 |
| #22558306 | 2 |
| C67×#1381 | 2 |
| #13151 | 67 |