Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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. #22578138 | C2 | semidirect |
| 2. #22577760 | C2 | semidirect |
| 3. #22577751 | C2 | semidirect |
| 4. #22577700 | C2 | semidirect |
| 5. #22577695 | C2 | semidirect |
| 6. #22577618 | C2 | semidirect |
| 8. Q8×#11764040 | C2 | semidirect |
| 9. C4×#14555498 | C2 | semidirect |
| 10. C4×#14555495 | C2 | semidirect |
| 11. #554×C137 | C2 | semidirect |
| 122. C137 | #3361 | semidirect |
| 125. #554 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578138 | 2 |
| #22577760 | 2 |
| #22577751 | 2 |
| #22577700 | 2 |
| #22577695 | 2 |
| #22577618 | 2 |
| #22577598 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555498 | 2 |
| C4×#14555495 | 2 |
| #554×C137 | 2 |
| #3361 | 137 |