Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #22577755 | C2 | semidirect |
| 3. #22577744 | C2 | semidirect |
| 4. #22577680 | C2 | semidirect |
| 5. #22577642 | C2 | semidirect |
| 6. #22577613 | C2 | semidirect |
| 7. #22577563 | C2 | semidirect |
| 8. C4×#14555497 | C2 | semidirect |
| 9. D4×#11764040 | C2 | semidirect |
| 10. #22577397 | C2 | semidirect |
| 11. #556×C137 | C2 | semidirect |
| 125. C137 | #3302 | semidirect |
| 127. #556 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578058 | 2 |
| #22577755 | 2 |
| #22577744 | 2 |
| #22577680 | 2 |
| #22577642 | 2 |
| #22577613 | 2 |
| #22577563 | 2 |
| C4×#14555497 | 2 |
| D4×#11764040 | 2 |
| #22577397 | 2 |
| #556×C137 | 2 |
| #3302 | 137 |