Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590620 | C2 | semidirect |
| 3. #22590474 | C2 | semidirect |
| 4. #22586399 | C2 | semidirect |
| 5. #22586300 | C2 | semidirect |
| 6. D4⋊(C71⋊C16) | C2 | semidirect |
| 7. C71×#1673 | C2 | semidirect |
| 133. #1673 | D71 | semidirect |
| 137. C71 | #12395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22600763 | 2 |
| #22590620 | 2 |
| #22590474 | 2 |
| #22586399 | 2 |
| #22586300 | 2 |
| D4⋊(C71⋊C16) | 2 |
| C71×#1673 | 2 |
| #12395 | 71 |