Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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×Dic274 | C2 | semidirect |
| 3. #22577750 | C2 | semidirect |
| 4. #22577748 | C2 | semidirect |
| 5. #22577693 | C2 | semidirect |
| 6. #22577692 | C2 | semidirect |
| 7. #22577603 | C2 | semidirect |
| 8. #22577601 | C2 | semidirect |
| 9. C8×Dic274 | C2 | semidirect |
| 10. #22577488 | C2 | semidirect |
| 11. C4×SD16×C137 | C2 | semidirect |
| 77. Dic274 | SD16 | semidirect |
| 91. Q8×C137 | #41 | semidirect |
| 125. C137 | #3362 | semidirect |
| 137. C4×SD16 | D137 | semidirect |
| 206. Q8 | #14555510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic274 | 2 |
| #22578074 | 2 |
| #22577750 | 2 |
| #22577748 | 2 |
| #22577693 | 2 |
| #22577692 | 2 |
| #22577603 | 2 |
| #22577601 | 2 |
| C8×Dic274 | 2 |
| #22577488 | 2 |
| C4×SD16×C137 | 2 |
| #3362 | 137 |