Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 10. #16863236 | C4 | direct (N × H) |
| 73. C4×C67 | Q64 | semidirect |
| 89. C67 | C4×Q64 | semidirect |
| 157. C4 | #16863236 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863236 | 2 |
| C4×Dic536 | 2 |
| #22558408 | 2 |
| #22558390 | 2 |
| #22558389 | 2 |
| C4×C67⋊C32 | 2 |
| C4×Q32×C67 | 2 |
| C4×Q64 | 67 |