Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
272 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #17984155 | C4 | semidirect |
| 14. C4⋊#11764047 | C4 | semidirect |
| 21. #17983999 | C4 | semidirect |
| 22. #17983998 | C4 | semidirect |
| 23. #17983998 | C4 | semidirect |
| 24. #97×C137 | C4 | semidirect |
| 72. #11764040 | C4⋊C4 | semidirect |
| 77. C8×C137 | C4⋊C4 | semidirect |
| 98. C137 | #1771 | semidirect |
| 121. #97 | #10587739 | semidirect |
| 176. C8 | C4⋊#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C2×#17984142 | 2 |
| C2×C8×#10587739 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578268 | 2 |
| #97×D137 | 2 |
| #1771 | 137 |