Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
412 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#17984142 | C2 | semidirect |
| 4. #22578268 | C2 | semidirect |
| 12. #17984145 | C4 | semidirect |
| 13. C22⋊#11764047 | C4 | semidirect |
| 17. C22⋊#11764040 | C4 | semidirect |
| 18. #17984000 | C4 | semidirect |
| 19. C22⋊C8×C137 | C4 | semidirect |
| 27. C2×#11764047 | C2×C4 | semidirect |
| 39. C2×#11764040 | C2×C4 | semidirect |
| 43. C2×C8×C137 | C2×C4 | semidirect |
| 75. C22×C137 | #97 | semidirect |
| 81. C2×D137 | #97 | semidirect |
| 99. C137 | #1749 | semidirect |
| 118. C22⋊C8 | #10587739 | semidirect |
| 140. C2×C8 | C2×#10587739 | semidirect |
| 184. C22 | #17984142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10587739 | 2 |
| #22578371 | 2 |
| C2×#17984142 | 2 |
| #22578268 | 2 |
| C22⋊C8×D137 | 2 |
| #1749 | 137 |