Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22600944 | C2 | semidirect |
| 2. #22590372 | C2 | semidirect |
| 3. #22587816 | C2 | semidirect |
| 4. #22586392 | C2 | semidirect |
| 5. #22586308 | C2 | semidirect |
| 6. #22586299 | C2 | semidirect |
| 7. C71×#2244 | C2 | semidirect |
| 154. #2244 | D71 | semidirect |
| 160. C71 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600944 | 2 |
| #22590372 | 2 |
| #22587816 | 2 |
| #22586392 | 2 |
| #22586308 | 2 |
| #22586299 | 2 |
| C71×#2244 | 2 |
| #12348 | 71 |