Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 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. #22601474 | C2 | semidirect |
| 2. #22590068 | C2 | semidirect |
| 3. #22589233 | C2 | semidirect |
| 4. #22586420 | C2 | semidirect |
| 5. C71×#3150 | C2 | semidirect |
| 26. C2×Dic284 | D4 | semidirect |
| 28. C2×D568 | D4 | semidirect |
| 36. C2×C71⋊C16 | D4 | semidirect |
| 165. #3150 | D71 | semidirect |
| 169. C71 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22590068 | 2 |
| #22589233 | 2 |
| #22586420 | 2 |
| C71×#3150 | 2 |
| #13340 | 71 |