Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590523 | C2 | semidirect |
| 2. #22590518 | C2 | semidirect |
| 3. #22589780 | C2 | semidirect |
| 4. #22586355 | C2 | semidirect |
| 5. #22586355 | C2 | semidirect |
| 6. #22586266 | C2 | semidirect |
| 8. C2×#14556062 | C22 | semidirect |
| 14. C22⋊(C71⋊C16) | C22 | semidirect |
| 15. C22⋊(C71⋊C16) | C22 | semidirect |
| 17. #17985764 | C22 | semidirect |
| 171. C71 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590523 | 2 |
| #22590518 | 2 |
| #22589780 | 2 |
| #22586355 | 2 |
| #22586266 | 2 |
| C71×#3199 | 2 |
| #12284 | 71 |