Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. C4×#11764040 | C4 | semidirect |
| 10. C8×Dic137 | C4 | semidirect |
| 11. C4×C8×C137 | C4 | semidirect |
| 33. #11764040 | C4⋊C4 | semidirect |
| 36. C8×C137 | C4⋊C4 | semidirect |
| 43. C4×C137 | #107 | semidirect |
| 45. Dic137 | #107 | semidirect |
| 52. C137 | #1845 | semidirect |
| 64. C4×C8 | #10587739 | semidirect |
| 89. C8 | C4⋊#10587739 | semidirect |
| 98. C4 | #17984157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984157 | 2 |
| #22578349 | 2 |
| C4×C8×D137 | 2 |
| #1845 | 137 |