Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590012 | C2 | semidirect |
| 2. #22589990 | C2 | semidirect |
| 3. #22588386 | C2 | semidirect |
| 4. #22588140 | C2 | semidirect |
| 15. C22×D8×C71 | C4 | semidirect |
| 22. #427×C71 | C4 | semidirect |
| 23. #418×C71 | C4 | semidirect |
| 173. C71 | #13231 | semidirect |
| 174. C22×D8 | Dic71 | semidirect |
| 182. #427 | Dic71 | semidirect |
| 183. #418 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590012 | 2 |
| #22589990 | 2 |
| #22588386 | 2 |
| #22588140 | 2 |
| C71×#3058 | 2 |
| #13231 | 71 |