Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22590025 | C2 | semidirect |
| 2. #22590005 | C2 | semidirect |
| 3. #22586500 | C2 | semidirect |
| 4. #22586497 | C2 | semidirect |
| 14. #532×C71 | C4 | semidirect |
| 17. #497×C71 | C4 | semidirect |
| 20. #496×C71 | C4 | semidirect |
| 22. C2×#97×C71 | C4 | semidirect |
| 178. C71 | #13577 | semidirect |
| 181. #532 | Dic71 | semidirect |
| 184. #497 | Dic71 | semidirect |
| 187. #496 | Dic71 | semidirect |
| 191. C2×#97 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590025 | 2 |
| #22590005 | 2 |
| #22586500 | 2 |
| #22586497 | 2 |
| C71×#3150 | 2 |
| #13577 | 71 |