Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
200 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #22578492 | C2 | direct (N × H) |
| 24. C2×#11764040 | C8 | semidirect |
| 25. C8×D137 | C8 | semidirect |
| 27. C2×C8×C137 | C8 | semidirect |
| 42. #11764040 | C2×C8 | semidirect |
| 44. C8×C137 | C2×C8 | semidirect |
| 58. C2×C137 | #334 | semidirect |
| 60. D137 | #334 | semidirect |
| 63. C137 | C2×#334 | semidirect |
| 87. C2×C8 | #11764049 | semidirect |
| 108. C8 | C2×#11764049 | semidirect |
| 125. C2 | #22578492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11764049 | 2 |
| #22578492 | 2 |
| C2×C8×#10587739 | 2 |
| C2×#334 | 137 |