Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
528 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 215 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. #22578516 | C2 | direct (N × H) |
| 2. C2×C4⋊#11764049 | C2 | semidirect |
| 4. C2×C4×#11764049 | C2 | semidirect |
| 7. C4⋊#11764049 | C22 | semidirect |
| 9. C4×#11764049 | C22 | semidirect |
| 37. C22×Dic137 | C8 | semidirect |
| 38. C2×C4×D137 | C8 | semidirect |
| 39. C2×C4×D137 | C8 | semidirect |
| 40. C2×C4×D137 | C8 | semidirect |
| 44. C22×C4×C137 | C8 | semidirect |
| 66. C2×Dic137 | C2×C8 | semidirect |
| 69. C4×D137 | C2×C8 | semidirect |
| 70. C4×D137 | C2×C8 | semidirect |
| 76. C2×C4×C137 | C2×C8 | semidirect |
| 99. C2×C137 | #431 | semidirect |
| 102. D137 | #431 | semidirect |
| 105. C137 | C2×#431 | semidirect |
| 142. C22×C4 | #11764049 | semidirect |
| 181. C2×C4 | C2×#11764049 | semidirect |
| 209. C2 | #22578516 | direct (N × H) |
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 |
| C2×C22⋊#11764049 | 2 |
| C2×C4×#11764049 | 2 |
| C22×C4×#10587739 | 2 |
| C2×#431 | 137 |