Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
752 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 3. #22578396 | C2 | direct (N × H) |
| 4. C2×#17984151 | C2 | semidirect |
| 16. #17984151 | C22 | semidirect |
| 18. C22×Dic274 | C4 | semidirect |
| 23. C2×Q8×D137 | C4 | semidirect |
| 24. C2×Q8×D137 | C4 | semidirect |
| 29. C22×Q8×C137 | C4 | semidirect |
| 48. C2×Dic274 | C2×C4 | semidirect |
| 57. Q8×D137 | C2×C4 | semidirect |
| 76. C2×Q8×C137 | C2×C4 | semidirect |
| 142. C2×C137 | #419 | semidirect |
| 145. D137 | #419 | semidirect |
| 147. C137 | C2×#419 | semidirect |
| 164. C22×Q8 | #10587739 | semidirect |
| 200. C2×Q8 | C2×#10587739 | semidirect |
| 293. C2 | #22578396 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D137⋊M16 | 2 |
| C2×#17984167 | 2 |
| #22578396 | 2 |
| C2×#17984151 | 2 |
| C22×Q8×D137 | 2 |
| C2×#419 | 137 |