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. #22577662 | C2 | semidirect |
| 5. #22577661 | C2 | semidirect |
| 6. #22577658 | C2 | semidirect |
| 7. #22577643 | C2 | semidirect |
| 8. #22577642 | C2 | semidirect |
| 9. #22577438 | C2 | semidirect |
| 10. #22577410 | C2 | semidirect |
| 11. #470×C137 | C2 | semidirect |
| 133. C137 | #3059 | semidirect |
| 141. #470 | 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×#17984096 | 2 |
| #22577976 | 2 |
| #22577662 | 2 |
| #22577661 | 2 |
| #22577658 | 2 |
| #22577643 | 2 |
| #22577642 | 2 |
| #22577438 | 2 |
| #22577410 | 2 |
| #470×C137 | 2 |
| #3059 | 137 |