Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22563853 | C2 | semidirect |
| 4. #22560143 | C2 | semidirect |
| 5. #22558780 | C2 | semidirect |
| 6. #22558057 | C2 | semidirect |
| 141. C22⋊C4×C67 | SD16 | semidirect |
| 239. C67 | #9949 | semidirect |
| 373. C22⋊C4 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570966 | 2 |
| C2×#16863534 | 2 |
| #22563853 | 2 |
| #22560143 | 2 |
| #22558780 | 2 |
| #22558057 | 2 |
| C67×#1964 | 2 |
| #9949 | 67 |