Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. C2×C4×#11764049 | C2 | semidirect |
| 4. (C2×#11764049)⋊C4 | C2 | semidirect |
| 7. C22×#11764049 | C4 | semidirect |
| 11. C22⋊#11764049 | C4 | semidirect |
| 33. C22⋊#10587739 | C8 | semidirect |
| 38. C22⋊Dic137 | C8 | semidirect |
| 39. #14555487 | C8 | semidirect |
| 40. C22⋊C4×C137 | C8 | semidirect |
| 43. #11764049 | C22⋊C4 | direct (N × H) |
| 51. C2×#10587739 | C2×C8 | semidirect |
| 62. C2×Dic137 | C2×C8 | semidirect |
| 66. C2×C4×C137 | C2×C8 | semidirect |
| 68. C22×C137 | C4×C8 | semidirect |
| 74. C2×D137 | C4×C8 | semidirect |
| 93. C137 | C8×C22⋊C4 | semidirect |
| 132. C22⋊C4 | #11764049 | direct (N × H) |
| 157. C2×C4 | C2×#11764049 | semidirect |
| 171. C22 | C4×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11764049 | 2 |
| C2×C22⋊#11764049 | 2 |
| C2×C4×#11764049 | 2 |
| (C2×#11764049)⋊C4 | 2 |
| C22⋊C4×#10587739 | 2 |
| C8×C22⋊C4 | 137 |