Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
514 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 83 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×#17985796 | C2 | semidirect |
| 2. C2×#17985739 | C2 | semidirect |
| 3. #22586488 | C2 | direct (N × H) |
| 8. #17985796 | C22 | semidirect |
| 10. #17985739 | C22 | semidirect |
| 177. C2×C71 | #1403 | semidirect |
| 183. C71 | C2×#1403 | semidirect |
| 355. C2 | #22586488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985796 | 2 |
| C2×#17985739 | 2 |
| #22586488 | 2 |
| C2×#455×C71 | 2 |
| C2×#1403 | 71 |