Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
770 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17986157 | C2 | semidirect |
| 4. #22589324 | C2 | semidirect |
| 5. #22588274 | C2 | semidirect |
| 6. #22586186 | C2 | semidirect |
| 238. C71 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599097 | 2 |
| C2×#17986157 | 2 |
| #22591999 | 2 |
| #22589324 | 2 |
| #22588274 | 2 |
| #22586186 | 2 |
| C71×#1519 | 2 |
| #9956 | 71 |