Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #22586643 | C2 | semidirect |
| 3. #22586315 | C2 | semidirect |
| 4. #22586312 | C2 | semidirect |
| 5. C71×#2165 | C2 | semidirect |
| 16. #17985720 | C22 | semidirect |
| 17. C8×C71⋊C8 | C22 | semidirect |
| 19. #364×C71 | C22 | semidirect |
| 57. Dic284 | M16 | semidirect |
| 61. D568 | M16 | semidirect |
| 126. #2165 | D71 | semidirect |
| 130. C71 | #11669 | semidirect |
| 141. #364 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597251 | 2 |
| #22586643 | 2 |
| #22586315 | 2 |
| #22586312 | 2 |
| C71×#2165 | 2 |
| #11669 | 71 |