Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22577883 | C2 | semidirect |
| 3. C2×#17984014 | C2 | semidirect |
| 4. #22577306 | C2 | semidirect |
| 5. #22577171 | C2 | semidirect |
| 6. #22577162 | C2 | semidirect |
| 7. #418×C137 | C2 | semidirect |
| 10. #17984114 | C4 | semidirect |
| 42. #14555494 | C2×C4 | semidirect |
| 58. C2×D4×C137 | C2×C4 | semidirect |
| 69. Dic274 | C22⋊C4 | semidirect |
| 71. D548 | C22⋊C4 | semidirect |
| 132. C137 | #1883 | semidirect |
| 137. #418 | D137 | semidirect |
| 174. C2×D4 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984114 | 2 |
| #22577883 | 2 |
| C2×#17984014 | 2 |
| #22577306 | 2 |
| #22577171 | 2 |
| #22577162 | 2 |
| #418×C137 | 2 |
| #1883 | 137 |