Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
316 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 11. #17984155 | C4 | semidirect |
| 12. C4⋊#11764047 | C4 | semidirect |
| 16. C4⋊#11764040 | C4 | semidirect |
| 17. #17984017 | C4 | semidirect |
| 18. C4⋊C8×C137 | C4 | semidirect |
| 27. C4×#10587739 | C8 | semidirect |
| 69. #10587739 | C4⋊C8 | direct (N × H) |
| 71. C4×C137 | C4×C8 | semidirect |
| 75. Dic137 | C4×C8 | semidirect |
| 83. C137 | C4×C4⋊C8 | semidirect |
| 101. C4⋊C8 | #10587739 | direct (N × H) |
| 159. C4 | C8×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C2×C8×#10587739 | 2 |
| C42×#10587739 | 2 |
| #22578268 | 2 |
| C4⋊C8×D137 | 2 |
| C4×C4⋊C8 | 137 |