Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4⋊#11764040 | C2 | semidirect |
| 3. C2×#17984017 | C2 | semidirect |
| 6. #22577157 | C2 | semidirect |
| 7. #336×C137 | C2 | semidirect |
| 43. #14555487 | C8 | semidirect |
| 72. C2×Dic137 | C2×C8 | semidirect |
| 85. C2×C4×C137 | C2×C8 | semidirect |
| 107. C2×D137 | C4⋊C8 | semidirect |
| 125. C137 | #1850 | semidirect |
| 133. #336 | D137 | semidirect |
| 209. C2×C4 | C8×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D137 | 2 |
| C2×C4⋊#11764040 | 2 |
| C2×#17984017 | 2 |
| C2×#17984000 | 2 |
| C4×#14555487 | 2 |
| #22577157 | 2 |
| #336×C137 | 2 |
| #1850 | 137 |