Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
716 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #22588275 | C2 | semidirect |
| 4. #22586207 | C2 | semidirect |
| 17. #395×C71 | C4 | semidirect |
| 18. #393×C71 | C4 | semidirect |
| 190. C71 | #9471 | semidirect |
| 200. #395 | Dic71 | semidirect |
| 201. #393 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597369 | 2 |
| #22588328 | 2 |
| #22588275 | 2 |
| #22586207 | 2 |
| C71×#2409 | 2 |
| #9471 | 71 |