Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597142 | C2 | semidirect |
| 3. C2×#17985810 | C2 | semidirect |
| 4. #22590057 | C2 | semidirect |
| 5. #22589216 | C2 | semidirect |
| 6. #22586446 | C2 | semidirect |
| 7. C71×#1377 | C2 | semidirect |
| 12. #17986437 | C4 | semidirect |
| 41. C2×D568 | C2×C4 | semidirect |
| 66. M32×C71 | C2×C4 | semidirect |
| 89. Dic284 | C22⋊C4 | semidirect |
| 97. D568 | C22⋊C4 | semidirect |
| 191. #1377 | D71 | semidirect |
| 192. C71 | #13025 | semidirect |
| 244. M32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986437 | 2 |
| #22597142 | 2 |
| C2×#17985810 | 2 |
| #22590057 | 2 |
| #22589216 | 2 |
| #22586446 | 2 |
| C71×#1377 | 2 |
| #13025 | 71 |