Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22558314 | C2 | semidirect |
| 4. #22558293 | C2 | semidirect |
| 5. C67×#3162 | C2 | semidirect |
| 21. C2×D536 | Q8 | semidirect |
| 120. #3162 | D67 | semidirect |
| 125. C67 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561924 | 2 |
| #22561085 | 2 |
| #22558314 | 2 |
| #22558293 | 2 |
| C67×#3162 | 2 |
| #13367 | 67 |