Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
944 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#17986137 | C2 | semidirect |
| 2. C2×#17985733 | C2 | semidirect |
| 3. #22586610 | C2 | semidirect |
| 4. #22586183 | C2 | semidirect |
| 24. C22×Dic142 | D4 | semidirect |
| 32. C22⋊(C71⋊C8) | D4 | semidirect |
| 89. C22×C4×C71 | SD16 | semidirect |
| 188. C71 | #9964 | semidirect |
| 269. C22×C4 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986137 | 2 |
| C2×#17985733 | 2 |
| #22586610 | 2 |
| #22586183 | 2 |
| C71×#2656 | 2 |
| #9964 | 71 |