Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#17984161 | C2 | semidirect |
| 2. C2×#17984159 | C2 | semidirect |
| 3. #22578318 | C2 | direct (N × H) |
| 7. #17984161 | C22 | semidirect |
| 10. #17984159 | C22 | semidirect |
| 78. C2×C137 | #359 | semidirect |
| 83. C137 | C2×#359 | semidirect |
| 165. C2 | #22578318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| C2×#17984159 | 2 |
| #22578318 | 2 |
| C2×#17984111 | 2 |
| C2×#359 | 137 |