Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
328 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22578489 | C2 | direct (N × H) |
| 28. C22×Dic137 | C8 | semidirect |
| 33. C2×C4×D137 | C8 | semidirect |
| 35. C22×C4×C137 | C8 | semidirect |
| 57. C2×Dic137 | C2×C8 | semidirect |
| 65. C2×C4×C137 | C2×C8 | semidirect |
| 90. C2×C137 | #324 | semidirect |
| 94. D137 | #324 | semidirect |
| 97. C137 | C2×#324 | semidirect |
| 129. C22×C4 | #11764049 | semidirect |
| 162. C2×C4 | C2×#11764049 | semidirect |
| 193. C2 | #22578489 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11764049 | 2 |
| #22578489 | 2 |
| C22×C4⋊#10587739 | 2 |
| C2×#324 | 137 |