Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14556069 | C2 | semidirect |
| 2. C2×#17986269 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. #22590055 | C2 | semidirect |
| 5. C2×#17985783 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#3058 | C2 | semidirect |
| 38. C2×D568 | D4 | semidirect |
| 47. C2×C71⋊C16 | D4 | semidirect |
| 49. #14556064 | D4 | semidirect |
| 202. #3058 | D71 | semidirect |
| 207. C71 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| C2×#17986269 | 2 |
| C2×#17985812 | 2 |
| #22590055 | 2 |
| C2×#17985783 | 2 |
| #22586435 | 2 |
| C71×#3058 | 2 |
| #13319 | 71 |