Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#17985822 | C2 | semidirect |
| 4. #22586439 | C2 | semidirect |
| 17. C22⋊C16×C71 | C4 | semidirect |
| 40. C2×C16×C71 | C2×C4 | semidirect |
| 103. C22×C71 | #365 | semidirect |
| 124. C71 | #12929 | semidirect |
| 135. C22⋊C16 | Dic71 | semidirect |
| 153. C2×C16 | C2×Dic71 | semidirect |
| 222. C22 | #17985822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556060 | 2 |
| C2×#17985822 | 2 |
| #22588378 | 2 |
| #22586439 | 2 |
| C71×#2112 | 2 |
| #12929 | 71 |