Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 191 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. D4×#11764049 | C2 | semidirect |
| 2. #22578516 | C2 | semidirect |
| 3. C2×C22⋊#11764049 | C2 | semidirect |
| 5. C22×#11764049 | C22 | semidirect |
| 6. C4⋊#11764049 | C22 | semidirect |
| 8. C22⋊#11764049 | C22 | semidirect |
| 9. C4×#11764049 | C22 | semidirect |
| 30. C2×D548 | C8 | semidirect |
| 31. C2×C22⋊D137 | C8 | semidirect |
| 32. D4×D137 | C8 | semidirect |
| 35. C2×D4×C137 | C8 | semidirect |
| 48. C22×D137 | C2×C8 | semidirect |
| 49. C22×D137 | C2×C8 | semidirect |
| 52. D548 | C2×C8 | semidirect |
| 53. C22⋊D137 | C2×C8 | semidirect |
| 54. C2×Dic137 | C2×C8 | semidirect |
| 55. C4×D137 | C2×C8 | semidirect |
| 57. C23×C137 | C2×C8 | semidirect |
| 58. D4×C137 | C2×C8 | semidirect |
| 59. C2×C4×C137 | C2×C8 | semidirect |
| 85. C137 | #2972 | semidirect |
| 108. C2×D4 | #11764049 | semidirect |
| 128. C23 | C2×#11764049 | semidirect |
| 131. D4 | C2×#11764049 | semidirect |
| 144. C2×C4 | C2×#11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11764049 | 2 |
| #22578516 | 2 |
| C2×C22⋊#11764049 | 2 |
| C2×D4×#10587739 | 2 |
| #2972 | 137 |