Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17986405 | C2 | semidirect |
| 3. #22589161 | C2 | semidirect |
| 4. C2×#17985740 | C2 | semidirect |
| 6. #22586222 | C2 | semidirect |
| 199. C71 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986405 | 2 |
| #22596391 | 2 |
| #22589161 | 2 |
| C2×#17985740 | 2 |
| C2×#17985739 | 2 |
| #22586222 | 2 |
| C2×#489×C71 | 2 |
| #10086 | 71 |