Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22601443 | C2 | semidirect |
| 2. #22590076 | C2 | semidirect |
| 3. #22588386 | C2 | semidirect |
| 4. #22586447 | C2 | semidirect |
| 16. #470×C71 | C4 | semidirect |
| 17. #469×C71 | C4 | semidirect |
| 24. #14556068 | D4 | semidirect |
| 144. C71 | #13077 | semidirect |
| 151. #470 | Dic71 | semidirect |
| 152. #469 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601443 | 2 |
| #22590076 | 2 |
| #22588386 | 2 |
| #22586447 | 2 |
| C71×#3060 | 2 |
| #13077 | 71 |