Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 13. #17984149 | C4 | semidirect |
| 18. #17984007 | C4 | semidirect |
| 19. #17984006 | C4 | semidirect |
| 20. #101×C137 | C4 | semidirect |
| 74. #10587739 | #101 | direct (N × H) |
| 84. C137 | C4×#101 | semidirect |
| 103. #101 | #10587739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10587739 | 2 |
| D137⋊#101 | 2 |
| M16×#10587739 | 2 |
| #22578282 | 2 |
| #101×D137 | 2 |
| C4×#101 | 137 |