Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
686 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 203 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×#17986401 | C2 | semidirect |
| 3. #22590582 | C2 | direct (N × H) |
| 4. C2×#17985801 | C2 | semidirect |
| 5. C2×#346×C71 | C2 | semidirect |
| 11. #17986401 | C22 | semidirect |
| 16. #17985801 | C22 | semidirect |
| 19. #346×C71 | C22 | semidirect |
| 98. C2×C71 | #2244 | semidirect |
| 106. C2×#346 | D71 | semidirect |
| 107. C71 | C2×#2244 | semidirect |
| 121. #346 | C2×D71 | semidirect |
| 200. C2 | #22590582 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986401 | 2 |
| C2×#17986376 | 2 |
| #22590582 | 2 |
| C2×#17985801 | 2 |
| C2×#346×C71 | 2 |
| C2×#2244 | 71 |