Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17986439 | C2 | semidirect |
| 2. C2×#17986275 | C2 | semidirect |
| 4. C2×#17985804 | C2 | semidirect |
| 5. C2×#17985782 | C2 | semidirect |
| 6. #22586450 | C2 | semidirect |
| 7. C2×#359×C71 | C2 | semidirect |
| 41. C2×Dic284 | D4 | semidirect |
| 59. #14556068 | D4 | semidirect |
| 80. #108×C71 | D4 | semidirect |
| 215. C2×#359 | D71 | semidirect |
| 219. C71 | #13308 | semidirect |
| 287. #108 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986439 | 2 |
| C2×#17986275 | 2 |
| #22598006 | 2 |
| C2×#17985804 | 2 |
| C2×#17985782 | 2 |
| #22586450 | 2 |
| C2×#359×C71 | 2 |
| #13308 | 71 |