Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #22578133 | C2 | semidirect |
| 3. #22577751 | C2 | semidirect |
| 4. #22577748 | C2 | semidirect |
| 5. #22577692 | C2 | semidirect |
| 6. #22577604 | C2 | semidirect |
| 7. #22577602 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 9. #22577490 | C2 | semidirect |
| 10. C4×#14555498 | C2 | semidirect |
| 11. #476×C137 | C2 | semidirect |
| 77. Dic274 | SD16 | semidirect |
| 78. Dic274 | #41 | semidirect |
| 125. C137 | #3362 | semidirect |
| 132. #476 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578133 | 2 |
| #22578074 | 2 |
| #22577751 | 2 |
| #22577748 | 2 |
| #22577692 | 2 |
| #22577604 | 2 |
| #22577602 | 2 |
| #22577527 | 2 |
| #22577490 | 2 |
| C4×#14555498 | 2 |
| #476×C137 | 2 |
| #3362 | 137 |