Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
376 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 2. #22558983 | C2 | semidirect |
| 5. #22558106 | C2 | semidirect |
| 6. #22558042 | C2 | semidirect |
| 7. C4×C4⋊C8×C67 | C2 | semidirect |
| 15. #16863143 | C4 | semidirect |
| 16. #16863139 | C4 | semidirect |
| 157. C4×C4⋊C8 | D67 | semidirect |
| 163. C67 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561037 | 2 |
| #22558983 | 2 |
| #22558859 | 2 |
| #22558607 | 2 |
| #22558106 | 2 |
| #22558042 | 2 |
| C4×C4⋊C8×C67 | 2 |
| #9577 | 67 |