Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22599647 | C2 | semidirect |
| 2. #22598431 | C2 | semidirect |
| 3. #22589139 | C2 | semidirect |
| 4. #22586952 | C2 | semidirect |
| 5. #22586951 | C2 | semidirect |
| 6. #22586209 | C2 | semidirect |
| 7. C71×#3109 | C2 | semidirect |
| 217. #3109 | D71 | semidirect |
| 222. C71 | #10026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599647 | 2 |
| #22598431 | 2 |
| #22589139 | 2 |
| #22586952 | 2 |
| #22586951 | 2 |
| #22586209 | 2 |
| C71×#3109 | 2 |
| #10026 | 71 |