Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #364×D71 | C2 | semidirect |
| 3. #22586625 | C2 | semidirect |
| 4. #22586317 | C2 | semidirect |
| 5. #22586316 | C2 | semidirect |
| 6. #22586315 | C2 | semidirect |
| 7. C71×#1336 | C2 | semidirect |
| 20. #17985820 | C22 | semidirect |
| 22. #17985720 | C22 | semidirect |
| 25. #364×C71 | C22 | semidirect |
| 26. #322×C71 | C22 | semidirect |
| 28. #14556151 | C8 | semidirect |
| 32. #14556147 | C8 | semidirect |
| 33. Q16×D71 | C8 | semidirect |
| 35. D8×D71 | C8 | semidirect |
| 187. #1336 | D71 | semidirect |
| 188. C71 | #11604 | semidirect |
| 204. #364 | C2×D71 | semidirect |
| 206. #322 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D71 | 2 |
| #364×D71 | 2 |
| #22586625 | 2 |
| #22586317 | 2 |
| #22586316 | 2 |
| #22586315 | 2 |
| C71×#1336 | 2 |
| #11604 | 71 |