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. #22577880 | C2 | semidirect |
| 4. #22577502 | C2 | semidirect |
| 5. #22577490 | C2 | semidirect |
| 6. #22577411 | C2 | semidirect |
| 8. #22577358 | C2 | semidirect |
| 9. #427×C137 | C2 | semidirect |
| 12. C2×#14555499 | C4 | semidirect |
| 17. #17984053 | C22 | semidirect |
| 23. #17984011 | C22 | semidirect |
| 25. #17983998 | C22 | semidirect |
| 26. C8×Dic137 | C22 | semidirect |
| 30. #107×C137 | C22 | semidirect |
| 31. #106×C137 | C22 | semidirect |
| 35. C2×Dic274 | C2×C4 | semidirect |
| 43. #14555499 | C2×C4 | semidirect |
| 44. #14555499 | C2×C4 | semidirect |
| 54. C2×C8×C137 | C2×C4 | semidirect |
| 103. C137 | #2949 | semidirect |
| 110. #427 | D137 | semidirect |
| 130. #107 | C2×D137 | semidirect |
| 131. #106 | C2×D137 | semidirect |
| 152. C2×C8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555499 | 2 |
| #22577880 | 2 |
| #22577877 | 2 |
| #22577502 | 2 |
| #22577490 | 2 |
| #22577411 | 2 |
| #22577407 | 2 |
| #22577358 | 2 |
| #427×C137 | 2 |
| #2949 | 137 |