Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#17984017 | C2 | semidirect |
| 4. #22577157 | C2 | semidirect |
| 24. C22×Dic137 | C8 | semidirect |
| 85. C22×C137 | C4⋊C8 | semidirect |
| 99. Dic137 | C22⋊C8 | semidirect |
| 108. C137 | #1797 | semidirect |
| 194. C22 | #17984017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic137 | 2 |
| C2×#17984017 | 2 |
| C2×C22⋊#11764040 | 2 |
| #22577157 | 2 |
| C2×C22⋊C8×C137 | 2 |
| #1797 | 137 |