Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
488 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 186 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. #22578426 | C2 | direct (N × H) |
| 2. C2×#17984155 | C2 | semidirect |
| 4. C2×#17984143 | C2 | semidirect |
| 7. #17984155 | C22 | semidirect |
| 9. #17984143 | C22 | semidirect |
| 79. C2×C137 | #432 | semidirect |
| 84. C137 | C2×#432 | semidirect |
| 165. C2 | #22578426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578426 | 2 |
| C2×#17984155 | 2 |
| C2×#17984145 | 2 |
| C2×#17984143 | 2 |
| C2×C42×D137 | 2 |
| C2×#432 | 137 |