Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
692 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17986310 | C2 | semidirect |
| 2. #22592812 | C2 | semidirect |
| 3. #22589177 | C2 | semidirect |
| 4. #22588427 | C2 | semidirect |
| 5. #22586908 | C2 | semidirect |
| 6. #22586187 | C2 | semidirect |
| 96. C22⋊Dic71 | D8 | semidirect |
| 234. C71 | #9952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986310 | 2 |
| #22592812 | 2 |
| #22589177 | 2 |
| #22588427 | 2 |
| #22586908 | 2 |
| #22586187 | 2 |
| C71×#3186 | 2 |
| #9952 | 71 |