Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
662 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×#14556073 | C2 | semidirect |
| 2. C22×#14556072 | C2 | semidirect |
| 4. C2×#17985799 | C2 | semidirect |
| 5. #22589199 | C2 | semidirect |
| 6. #22586417 | C2 | semidirect |
| 7. C2×#357×C71 | C2 | semidirect |
| 37. C2×Dic284 | D4 | semidirect |
| 55. C2×C71⋊C16 | D4 | semidirect |
| 71. C2×C16×C71 | D4 | semidirect |
| 158. C2×Dic71 | SD32 | semidirect |
| 206. C2×#357 | D71 | semidirect |
| 209. C71 | #13328 | semidirect |
| 269. C2×C16 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556073 | 2 |
| C22×#14556072 | 2 |
| C2×#17986374 | 2 |
| C2×#17985799 | 2 |
| #22589199 | 2 |
| #22586417 | 2 |
| C2×#357×C71 | 2 |
| #13328 | 71 |