Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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. #17984159 | C4 | semidirect |
| 10. #17984158 | C4 | semidirect |
| 17. #17984024 | C4 | semidirect |
| 18. #17984023 | C4 | semidirect |
| 19. #108×C137 | C4 | semidirect |
| 64. #10587739 | #108 | direct (N × H) |
| 73. C137 | C4×#108 | semidirect |
| 89. #108 | #10587739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| M16×#10587739 | 2 |
| C2×C8×#10587739 | 2 |
| #22578278 | 2 |
| #108×D137 | 2 |
| C4×#108 | 137 |