Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. Q8×D548 | C2 | semidirect |
| 3. #22577754 | C2 | semidirect |
| 4. #22577735 | C2 | semidirect |
| 5. #22577688 | C2 | semidirect |
| 6. #22577631 | C2 | semidirect |
| 7. #22577608 | C2 | semidirect |
| 8. #22577540 | C2 | semidirect |
| 9. C8×D548 | C2 | semidirect |
| 10. #103×D137 | C2 | semidirect |
| 11. C4×SD16×C137 | C2 | semidirect |
| 82. D548 | SD16 | semidirect |
| 94. Q8×C137 | #41 | semidirect |
| 128. C137 | #3298 | semidirect |
| 138. C4×SD16 | D137 | semidirect |
| 213. Q8 | #14555510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D548 | 2 |
| #22578058 | 2 |
| #22577754 | 2 |
| #22577735 | 2 |
| #22577688 | 2 |
| #22577631 | 2 |
| #22577608 | 2 |
| #22577540 | 2 |
| C8×D548 | 2 |
| #103×D137 | 2 |
| C4×SD16×C137 | 2 |
| #3298 | 137 |