Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×Dic274 | C2 | semidirect |
| 3. #22577739 | C2 | semidirect |
| 5. #22577711 | C2 | semidirect |
| 6. #22577626 | C2 | semidirect |
| 7. #22577561 | C2 | semidirect |
| 9. #22577511 | C2 | semidirect |
| 10. #22577505 | C2 | semidirect |
| 11. #432×C137 | C2 | semidirect |
| 131. C137 | #3117 | semidirect |
| 143. #432 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577937 | 2 |
| C2×C4×Dic274 | 2 |
| #22577739 | 2 |
| #22577722 | 2 |
| #22577711 | 2 |
| #22577626 | 2 |
| #22577561 | 2 |
| #22577544 | 2 |
| #22577511 | 2 |
| #22577505 | 2 |
| #432×C137 | 2 |
| #3117 | 137 |