Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 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. C2×#17985963 | C2 | semidirect |
| 2. #22588250 | C2 | semidirect |
| 4. C22×#11765849 | C22 | semidirect |
| 6. C2×C22⋊(C71⋊C8) | C22 | semidirect |
| 14. C22×C71⋊C8 | C23 | semidirect |
| 41. C24×C71 | M16 | semidirect |
| 91. C22×C71 | #407 | semidirect |
| 105. C71 | #20579 | semidirect |
| 141. C24 | #11765849 | semidirect |
| 193. C22 | #17985963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985963 | 2 |
| #22588250 | 2 |
| C25×C4×C71 | 2 |
| #20579 | 71 |