Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
248 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22578487 | C2 | direct (N × H) |
| 15. #14555518 | C8 | semidirect |
| 17. C2×#11764047 | C8 | semidirect |
| 22. C2×#11764040 | C8 | semidirect |
| 23. C8×D137 | C8 | semidirect |
| 25. C2×C8×C137 | C8 | semidirect |
| 30. #11764047 | C2×C8 | semidirect |
| 37. #11764040 | C2×C8 | semidirect |
| 39. C8×C137 | C2×C8 | semidirect |
| 50. C2×C137 | #322 | semidirect |
| 52. D137 | #322 | semidirect |
| 54. C137 | C2×#322 | semidirect |
| 77. C2×C8 | #11764049 | semidirect |
| 94. C8 | C2×#11764049 | semidirect |
| 107. C2 | #22578487 | 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 |
| #22578487 | 2 |
| C2×C8×#10587739 | 2 |
| C2×#322 | 137 |