Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
184 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22578506 | C2 | semidirect |
| 3. C4⋊#14555522 | C2 | semidirect |
| 39. C4×D137 | C16 | semidirect |
| 51. C4×C137 | C2×C16 | semidirect |
| 53. Dic137 | C2×C16 | semidirect |
| 59. D137 | C4⋊C16 | semidirect |
| 60. C137 | C2×C4⋊C16 | semidirect |
| 116. C4 | #17984183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984183 | 2 |
| #22578506 | 2 |
| C4⋊#14555522 | 2 |
| C4×#14555518 | 2 |
| C2×C4⋊C16 | 137 |