Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984118 | C2 | semidirect |
| 3. C2×#17984076 | C2 | semidirect |
| 4. #22577625 | C2 | semidirect |
| 5. #22577618 | C2 | semidirect |
| 6. #22577427 | C2 | semidirect |
| 7. #22577411 | C2 | semidirect |
| 8. #22577407 | C2 | semidirect |
| 9. C4×#41×C137 | C2 | semidirect |
| 14. C2×#14555500 | C22 | semidirect |
| 15. C2×#14555498 | C22 | semidirect |
| 24. C4⋊#11764040 | C22 | semidirect |
| 25. #17984011 | C22 | semidirect |
| 28. C4×Q8×C137 | C22 | semidirect |
| 30. C4×D4×C137 | C22 | semidirect |
| 125. C137 | #3040 | semidirect |
| 130. C4×#41 | D137 | semidirect |
| 150. C4×Q8 | C2×D137 | semidirect |
| 152. C4×D4 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984118 | 2 |
| C2×#17984113 | 2 |
| C2×#17984076 | 2 |
| #22577625 | 2 |
| #22577618 | 2 |
| #22577427 | 2 |
| #22577411 | 2 |
| #22577407 | 2 |
| C4×#41×C137 | 2 |
| #3040 | 137 |