Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 5. #17984143 | C4 | direct (N × H) |
| 6. C4×#11764047 | C4 | semidirect |
| 24. #11764047 | C42 | semidirect |
| 45. C4×C137 | #97 | semidirect |
| 47. Dic137 | #97 | semidirect |
| 54. C137 | C4×#97 | semidirect |
| 103. C4 | #17984143 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984143 | 2 |
| C2×C4×#11764047 | 2 |
| C42×Dic137 | 2 |
| C4×#97 | 137 |