Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22577881 | C2 | semidirect |
| 4. #22577506 | C2 | semidirect |
| 5. #22577488 | C2 | semidirect |
| 6. #22577439 | C2 | semidirect |
| 8. #22577361 | C2 | semidirect |
| 9. #419×C137 | C2 | semidirect |
| 11. C2×#14555497 | C4 | semidirect |
| 16. Q8×Dic137 | C22 | semidirect |
| 23. #17984021 | C22 | semidirect |
| 24. #17984019 | C22 | semidirect |
| 26. #17983998 | C22 | semidirect |
| 27. C8×Dic137 | C22 | semidirect |
| 31. #103×C137 | C22 | semidirect |
| 38. #14555497 | C2×C4 | semidirect |
| 39. #14555497 | C2×C4 | semidirect |
| 40. C2×#11764040 | C2×C4 | semidirect |
| 54. C2×Q8×C137 | C2×C4 | semidirect |
| 103. C137 | #2949 | semidirect |
| 111. #419 | D137 | semidirect |
| 132. #103 | C2×D137 | semidirect |
| 139. C2×Q8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| #22577881 | 2 |
| #22577877 | 2 |
| #22577506 | 2 |
| #22577488 | 2 |
| #22577439 | 2 |
| #22577409 | 2 |
| #22577361 | 2 |
| #419×C137 | 2 |
| #2949 | 137 |