Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D137 | C2 | semidirect |
| 4. #22577660 | C2 | semidirect |
| 5. #22577659 | C2 | semidirect |
| 6. #22577645 | C2 | semidirect |
| 7. #22577644 | C2 | semidirect |
| 8. #22577641 | C2 | semidirect |
| 9. #22577440 | C2 | semidirect |
| 10. #22577410 | C2 | semidirect |
| 11. #467×C137 | C2 | semidirect |
| 137. C137 | #3059 | semidirect |
| 147. #467 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D137 | 2 |
| C2×#17984094 | 2 |
| #22577976 | 2 |
| #22577660 | 2 |
| #22577659 | 2 |
| #22577645 | 2 |
| #22577644 | 2 |
| #22577641 | 2 |
| #22577440 | 2 |
| #22577410 | 2 |
| #467×C137 | 2 |
| #3059 | 137 |