Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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. #17984034 | C4 | direct (N × H) |
| 55. C4×C137 | Q32 | semidirect |
| 63. C137 | C4×Q32 | semidirect |
| 121. C4 | #17984034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984034 | 2 |
| C4×Dic548 | 2 |
| #22577228 | 2 |
| #22577207 | 2 |
| #22577206 | 2 |
| C4×#14555485 | 2 |
| C4×Q16×C137 | 2 |
| C4×Q32 | 137 |