Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590099 | C2 | semidirect |
| 3. #22590047 | C2 | semidirect |
| 4. #22590045 | C2 | semidirect |
| 5. #22589238 | C2 | semidirect |
| 6. #22586441 | C2 | semidirect |
| 7. C71×#1976 | C2 | semidirect |
| 183. #1976 | D71 | semidirect |
| 185. C71 | #13447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22590099 | 2 |
| #22590047 | 2 |
| #22590045 | 2 |
| #22589238 | 2 |
| #22586441 | 2 |
| C71×#1976 | 2 |
| #13447 | 71 |