Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. #22590660 | C2 | semidirect |
| 3. #22590657 | C2 | semidirect |
| 4. #22590449 | C2 | semidirect |
| 5. #22586526 | C2 | semidirect |
| 6. #22586479 | C2 | semidirect |
| 7. C71×#1418 | C2 | semidirect |
| 15. C2×Dic568 | C22 | semidirect |
| 22. #17985833 | C22 | semidirect |
| 25. M64×C71 | C22 | semidirect |
| 26. #367×C71 | C22 | semidirect |
| 146. #1418 | D71 | semidirect |
| 148. C71 | #13668 | semidirect |
| 165. M64 | C2×D71 | semidirect |
| 166. #367 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601473 | 2 |
| #22590660 | 2 |
| #22590657 | 2 |
| #22590449 | 2 |
| #22586526 | 2 |
| #22586479 | 2 |
| C71×#1418 | 2 |
| #13668 | 71 |