Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577960 | C2 | semidirect |
| 2. #22577762 | C2 | semidirect |
| 3. #22577757 | C2 | semidirect |
| 4. #22577412 | C2 | semidirect |
| 6. C4×#14555494 | C2 | semidirect |
| 9. #17984088 | C22 | semidirect |
| 10. #17984080 | C22 | semidirect |
| 14. #17984012 | C22 | semidirect |
| 16. #17983999 | C22 | semidirect |
| 17. C4×#11764040 | C22 | semidirect |
| 83. C137 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577960 | 2 |
| #22577762 | 2 |
| #22577757 | 2 |
| #22577412 | 2 |
| #22577408 | 2 |
| C4×#14555494 | 2 |
| C2×#124×C137 | 2 |
| #3140 | 137 |