Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22578487 | C2 | semidirect |
| 4. C8×#11764049 | C2 | semidirect |
| 24. #14555520 | C8 | semidirect |
| 25. #14555519 | C8 | semidirect |
| 32. #14555494 | C8 | semidirect |
| 33. #14555493 | C8 | semidirect |
| 35. M16×C137 | C8 | semidirect |
| 38. #11764049 | M16 | direct (N × H) |
| 45. #11764047 | C2×C8 | semidirect |
| 52. #11764040 | C2×C8 | semidirect |
| 54. C8×C137 | C2×C8 | semidirect |
| 73. C137 | C8×M16 | semidirect |
| 99. M16 | #11764049 | direct (N × H) |
| 128. C8 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578516 | 2 |
| C2×C4×#11764049 | 2 |
| #22578487 | 2 |
| C8×#11764049 | 2 |
| M16×#10587739 | 2 |
| C8×M16 | 137 |