Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22596930 | C2 | semidirect |
| 3. #22590057 | C2 | semidirect |
| 4. #22586446 | C2 | semidirect |
| 5. C2×#349×C71 | C2 | semidirect |
| 10. #17986252 | C4 | semidirect |
| 25. C2×D568 | C2×C4 | semidirect |
| 38. #14556062 | D4 | semidirect |
| 42. #14556060 | C2×C4 | semidirect |
| 160. C2×#349 | D71 | semidirect |
| 162. C71 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986252 | 2 |
| #22596930 | 2 |
| #22590057 | 2 |
| #22586446 | 2 |
| C2×#349×C71 | 2 |
| #12999 | 71 |