Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16863213 | C2 | semidirect |
| 5. #22561070 | C2 | semidirect |
| 6. #22558318 | C2 | semidirect |
| 7. C67×#1376 | C2 | semidirect |
| 12. #16863839 | C4 | semidirect |
| 184. #1376 | D67 | semidirect |
| 185. C67 | #13028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863839 | 2 |
| C2×#16863514 | 2 |
| C2×#16863213 | 2 |
| #22561922 | 2 |
| #22561070 | 2 |
| #22558318 | 2 |
| C67×#1376 | 2 |
| #13028 | 67 |