Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
388 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C22×#11765849 | C4 | semidirect |
| 7. C2×C22⋊(C71⋊C8) | C4 | semidirect |
| 14. #343×C71 | C4 | semidirect |
| 148. C71 | #7282 | semidirect |
| 157. #343 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588638 | 2 |
| C4×#14556043 | 2 |
| C4×#100×C71 | 2 |
| #7282 | 71 |