Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
184 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22578324 | C2 | semidirect |
| 3. C4⋊#14555513 | C2 | semidirect |
| 34. C4×D137 | C16 | semidirect |
| 50. C4×C137 | C2×C16 | semidirect |
| 55. Dic137 | C2×C16 | semidirect |
| 59. D137 | C4⋊C16 | semidirect |
| 60. C137 | C2×C4⋊C16 | semidirect |
| 114. C4 | #17984161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| #22578324 | 2 |
| C4⋊#14555513 | 2 |
| C4×C8×D137 | 2 |
| C2×C4⋊C16 | 137 |