Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 7. #17984157 | C4 | direct (N × H) |
| 12. C4×#11764040 | C4 | semidirect |
| 13. C8×Dic137 | C4 | semidirect |
| 14. C8×Dic137 | C4 | semidirect |
| 15. C4×C8×C137 | C4 | semidirect |
| 46. #11764040 | C42 | semidirect |
| 51. C8×C137 | C42 | semidirect |
| 59. C4×C137 | #107 | semidirect |
| 63. Dic137 | #107 | semidirect |
| 70. C137 | C4×#107 | semidirect |
| 85. C4×C8 | #10587739 | semidirect |
| 122. C8 | C4×#10587739 | semidirect |
| 133. C4 | #17984157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984157 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578277 | 2 |
| C4×C8×D137 | 2 |
| C4×#107 | 137 |