Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
|---|---|---|
| 2. #22578346 | C2 | direct (N × H) |
| 3. C2×(C2×#10587739)⋊C4 | C2 | semidirect |
| 8. (C2×#10587739)⋊C4 | C22 | semidirect |
| 10. C23×Dic137 | C4 | semidirect |
| 12. C22×C4×D137 | C4 | semidirect |
| 13. C22×C4×D137 | C4 | semidirect |
| 16. C23×C4×C137 | C4 | semidirect |
| 29. C22×Dic137 | C2×C4 | semidirect |
| 35. C2×C4×D137 | C2×C4 | semidirect |
| 40. C22×C4×C137 | C2×C4 | semidirect |
| 89. C2×C137 | #381 | semidirect |
| 93. D137 | #381 | semidirect |
| 95. C137 | C2×#381 | semidirect |
| 109. C23×C4 | #10587739 | semidirect |
| 135. C22×C4 | C2×#10587739 | semidirect |
| 188. C2 | #22578346 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#10587739 | 2 |
| #22578346 | 2 |
| C2×(C2×#10587739)⋊C4 | 2 |
| C23×C4×D137 | 2 |
| C2×#381 | 137 |