Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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. #22561983 | C2 | semidirect |
| 4. C2×#16863220 | C2 | semidirect |
| 7. #16863813 | C4 | semidirect |
| 22. #14523983 | C2×C4 | semidirect |
| 24. C2×C67⋊C16 | C2×C4 | semidirect |
| 89. C67 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573312 | 2 |
| #22568804 | 2 |
| #22561983 | 2 |
| C2×#16863220 | 2 |
| C67×#2916 | 2 |
| #33404 | 67 |