Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
296 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 10. C4×#11764047 | C4 | semidirect |
| 11. C4×#11764047 | C4 | semidirect |
| 16. C4⋊#11764040 | C4 | semidirect |
| 17. #17984017 | C4 | semidirect |
| 18. C4⋊C8×C137 | C4 | semidirect |
| 26. C4⋊#10587739 | C8 | semidirect |
| 44. #11764047 | C4⋊C4 | semidirect |
| 67. C4×C137 | C4×C8 | semidirect |
| 71. Dic137 | C4×C8 | semidirect |
| 79. C137 | C8×C4⋊C4 | semidirect |
| 94. C4⋊C8 | #10587739 | semidirect |
| 151. C4 | C8×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555518 | 2 |
| C2×C8×#10587739 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578268 | 2 |
| C4⋊C8×D137 | 2 |
| C8×C4⋊C4 | 137 |