Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22590128 | C2 | semidirect |
| 4. #22589126 | C2 | semidirect |
| 5. #22586437 | C2 | semidirect |
| 6. #22586430 | C2 | semidirect |
| 25. #361×C71 | C4 | semidirect |
| 59. M32×C71 | C2×C4 | semidirect |
| 62. #108×C71 | C2×C4 | semidirect |
| 167. C71 | #12940 | semidirect |
| 183. #361 | Dic71 | semidirect |
| 205. M32 | C2×Dic71 | semidirect |
| 211. #108 | C2×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597192 | 2 |
| #22590128 | 2 |
| C2×#17985800 | 2 |
| #22589126 | 2 |
| #22586437 | 2 |
| #22586430 | 2 |
| C2×#361×C71 | 2 |
| #12940 | 71 |