Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
384 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. C2×C4×#11764047 | C2 | semidirect |
| 4. #22578269 | C2 | semidirect |
| 7. C2×#14555518 | C4 | semidirect |
| 11. #17984145 | C4 | semidirect |
| 33. #14555487 | C8 | semidirect |
| 40. #11764047 | C22⋊C4 | semidirect |
| 48. C2×Dic137 | C2×C8 | semidirect |
| 61. C2×C4×C137 | C2×C8 | semidirect |
| 71. C2×D137 | C4×C8 | semidirect |
| 84. C137 | C8×C22⋊C4 | semidirect |
| 143. C2×C4 | #14555518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555518 | 2 |
| C2×#17984145 | 2 |
| C2×C4×#11764047 | 2 |
| #22578269 | 2 |
| #22577250 | 2 |
| C8×C22⋊C4 | 137 |