Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1502 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 907 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. #22588027 | C2 | semidirect |
| 5. C4×#11765849 | C4 | semidirect |
| 14. #14556039 | C2×C4 | semidirect |
| 15. C4×C71⋊C8 | C2×C4 | semidirect |
| 58. C71 | #20329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765849 | 2 |
| #22588027 | 2 |
| C2×#376×C71 | 2 |
| #20329 | 71 |