Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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×#17985827 | C2 | semidirect |
| 3. C2×#17985801 | C2 | semidirect |
| 4. #22589206 | C2 | semidirect |
| 5. C2×#346×C71 | C2 | semidirect |
| 9. C2×D1136 | C4 | semidirect |
| 72. C16×C71 | C22⋊C4 | semidirect |
| 122. C2×#346 | D71 | semidirect |
| 124. C71 | #13239 | semidirect |
| 191. C16 | (C2×D71)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1136 | 2 |
| C2×#17985827 | 2 |
| C2×#17985801 | 2 |
| #22589206 | 2 |
| C2×#346×C71 | 2 |
| #13239 | 71 |