Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
780 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 95 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×#17986386 | C2 | semidirect |
| 2. #22596386 | C2 | semidirect |
| 3. C2×#17985738 | C2 | semidirect |
| 4. #22586221 | C2 | semidirect |
| 5. C71×#1961 | C2 | semidirect |
| 36. #14556039 | D4 | semidirect |
| 43. #127×C71 | D4 | semidirect |
| 148. #1961 | D71 | semidirect |
| 151. C71 | #10078 | semidirect |
| 179. #127 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986386 | 2 |
| #22596386 | 2 |
| C2×#17985738 | 2 |
| #22586221 | 2 |
| C71×#1961 | 2 |
| #10078 | 71 |