Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #22578123 | C2 | semidirect |
| 2. #22577749 | C2 | semidirect |
| 3. #22577724 | C2 | semidirect |
| 4. #22577688 | C2 | semidirect |
| 5. #22577630 | C2 | semidirect |
| 6. #22577600 | C2 | semidirect |
| 7. #22577565 | C2 | semidirect |
| 8. C4×#14555500 | C2 | semidirect |
| 9. D4×#11764040 | C2 | semidirect |
| 10. #22577399 | C2 | semidirect |
| 127. C137 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578123 | 2 |
| #22577749 | 2 |
| #22577724 | 2 |
| #22577688 | 2 |
| #22577630 | 2 |
| #22577600 | 2 |
| #22577565 | 2 |
| C4×#14555500 | 2 |
| D4×#11764040 | 2 |
| #22577399 | 2 |
| #550×C137 | 2 |
| #3304 | 137 |