Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589961 | C2 | semidirect |
| 2. #22588386 | C2 | semidirect |
| 3. #22586328 | C2 | semidirect |
| 4. #22586325 | C2 | semidirect |
| 12. C2×#135×C71 | C4 | semidirect |
| 15. #470×C71 | C4 | semidirect |
| 17. #469×C71 | C4 | semidirect |
| 21. C2×#106×C71 | C4 | semidirect |
| 177. C71 | #11867 | semidirect |
| 178. C2×#135 | Dic71 | semidirect |
| 182. #470 | Dic71 | semidirect |
| 184. #469 | Dic71 | semidirect |
| 189. C2×#106 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589961 | 2 |
| #22588386 | 2 |
| #22586328 | 2 |
| #22586325 | 2 |
| C71×#3060 | 2 |
| #11867 | 71 |