Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 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×#17984107 | C2 | semidirect |
| 2. C2×#17984096 | C2 | semidirect |
| 3. #22577982 | C2 | semidirect |
| 4. #22577662 | C2 | semidirect |
| 5. #22577661 | C2 | semidirect |
| 6. #22577653 | C2 | semidirect |
| 7. #22577631 | C2 | semidirect |
| 8. #22577630 | C2 | semidirect |
| 9. #106×D137 | C2 | semidirect |
| 10. #22577401 | C2 | semidirect |
| 11. #469×C137 | C2 | semidirect |
| 64. C8×D137 | D4 | semidirect |
| 139. C137 | #3060 | semidirect |
| 147. #469 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984107 | 2 |
| C2×#17984096 | 2 |
| #22577982 | 2 |
| #22577662 | 2 |
| #22577661 | 2 |
| #22577653 | 2 |
| #22577631 | 2 |
| #22577630 | 2 |
| #106×D137 | 2 |
| #22577401 | 2 |
| #469×C137 | 2 |
| #3060 | 137 |