Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #22586352 | C2 | semidirect |
| 11. C22×Q16×C71 | C4 | semidirect |
| 16. #467×C71 | C4 | semidirect |
| 18. C2×#107×C71 | C4 | semidirect |
| 152. C71 | #11706 | semidirect |
| 153. C22×Q16 | Dic71 | semidirect |
| 160. #467 | Dic71 | semidirect |
| 162. C2×#107 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589951 | 2 |
| #22588057 | 2 |
| #22586352 | 2 |
| C2×#467×C71 | 2 |
| #11706 | 71 |