Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17986437 | C2 | semidirect |
| 2. C2×#17986435 | C2 | semidirect |
| 3. C2×#17986374 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22589226 | C2 | semidirect |
| 6. #22586421 | C2 | semidirect |
| 7. C2×#361×C71 | C2 | semidirect |
| 38. C2×Dic284 | D4 | semidirect |
| 46. C2×D568 | D4 | semidirect |
| 59. #14556068 | D4 | semidirect |
| 75. M32×C71 | D4 | semidirect |
| 210. C2×#361 | D71 | semidirect |
| 213. C71 | #13331 | semidirect |
| 276. M32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| C2×#17986435 | 2 |
| C2×#17986374 | 2 |
| C2×#17985811 | 2 |
| #22589226 | 2 |
| #22586421 | 2 |
| C2×#361×C71 | 2 |
| #13331 | 71 |