Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #22577755 | C2 | semidirect |
| 4. #22577707 | C2 | semidirect |
| 7. #22577613 | C2 | semidirect |
| 8. Q8×#11764040 | C2 | semidirect |
| 9. C4×#14555500 | C2 | semidirect |
| 11. #557×C137 | C2 | semidirect |
| 115. C137 | #3364 | semidirect |
| 117. #557 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578126 | 2 |
| #22577760 | 2 |
| #22577755 | 2 |
| #22577707 | 2 |
| #22577680 | 2 |
| #22577625 | 2 |
| #22577613 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555500 | 2 |
| C4×#14555497 | 2 |
| #557×C137 | 2 |
| #3364 | 137 |