Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
304 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22590156 | C2 | semidirect |
| 2. #22588095 | C2 | semidirect |
| 3. #22586334 | C2 | semidirect |
| 5. #22586328 | C2 | semidirect |
| 17. #498×C71 | C4 | semidirect |
| 18. #495×C71 | C4 | semidirect |
| 23. #442×C71 | C4 | semidirect |
| 24. #441×C71 | C4 | semidirect |
| 152. C71 | #11769 | semidirect |
| 154. #498 | Dic71 | semidirect |
| 155. #495 | Dic71 | semidirect |
| 160. #442 | Dic71 | semidirect |
| 161. #441 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590156 | 2 |
| #22588095 | 2 |
| #22586334 | 2 |
| #22586331 | 2 |
| #22586328 | 2 |
| #22586325 | 2 |
| C71×#3173 | 2 |
| #11769 | 71 |