Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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×#17984163 | C2 | semidirect |
| 2. #22578413 | C2 | semidirect |
| 3. #22578320 | C2 | semidirect |
| 4. #22578319 | C2 | semidirect |
| 8. #17984163 | C22 | semidirect |
| 11. #17984156 | C22 | semidirect |
| 14. #17984110 | C4 | semidirect |
| 18. Q16×D137 | C4 | semidirect |
| 20. D8×D137 | C4 | semidirect |
| 22. #135×C137 | C4 | semidirect |
| 102. C137 | #2145 | semidirect |
| 115. #135 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984163 | 2 |
| #22578413 | 2 |
| #22578320 | 2 |
| #22578319 | 2 |
| #135×D137 | 2 |
| #2145 | 137 |