Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17986046 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. C2×#17985780 | C2 | semidirect |
| 6. #22586438 | C2 | semidirect |
| 7. C71×#1383 | C2 | semidirect |
| 54. #14556064 | D4 | semidirect |
| 64. #108×C71 | D4 | semidirect |
| 185. #1383 | D71 | semidirect |
| 186. C71 | #13010 | semidirect |
| 242. #108 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986253 | 2 |
| C2×#17986046 | 2 |
| C2×#17985813 | 2 |
| C2×#17985811 | 2 |
| C2×#17985780 | 2 |
| #22586438 | 2 |
| C71×#1383 | 2 |
| #13010 | 71 |