Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#17984142 | C2 | semidirect |
| 4. #22578268 | C2 | semidirect |
| 7. C2×#14555518 | C4 | semidirect |
| 10. C22×#11764047 | C4 | semidirect |
| 17. C22⋊#11764040 | C4 | semidirect |
| 18. #17984000 | C4 | semidirect |
| 19. C22⋊C8×C137 | C4 | semidirect |
| 47. #11764047 | C22⋊C4 | semidirect |
| 71. C22×C137 | #97 | semidirect |
| 76. C2×D137 | #97 | semidirect |
| 92. C137 | #1752 | semidirect |
| 110. C22⋊C8 | #10587739 | semidirect |
| 171. C22 | #17984142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555518 | 2 |
| C2×#17984142 | 2 |
| C4×C22⋊#10587739 | 2 |
| #22578268 | 2 |
| C22⋊C8×D137 | 2 |
| #1752 | 137 |