Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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 | semidirect |
| 3. C8×#11764049 | C2 | semidirect |
| 17. #14555518 | C8 | semidirect |
| 20. C2×#11764047 | C8 | semidirect |
| 25. C2×#11764040 | C8 | semidirect |
| 26. C8×D137 | C8 | semidirect |
| 27. C8×D137 | C8 | semidirect |
| 30. C2×C8×C137 | C8 | semidirect |
| 62. C137 | #1450 | semidirect |
| 90. C2×C8 | #11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578516 | 2 |
| #22578487 | 2 |
| C8×#11764049 | 2 |
| C2×C8×#10587739 | 2 |
| #1450 | 137 |