Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22601490 | C2 | semidirect |
| 2. #22600145 | C2 | semidirect |
| 3. #22590593 | C2 | semidirect |
| 4. #22590466 | C2 | semidirect |
| 5. #22590421 | C2 | semidirect |
| 6. #22590319 | C2 | semidirect |
| 7. #22590178 | C2 | semidirect |
| 8. C71×#2178 | C2 | semidirect |
| 145. #2178 | D71 | semidirect |
| 147. C71 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601490 | 2 |
| #22600145 | 2 |
| #22590593 | 2 |
| #22590466 | 2 |
| #22590421 | 2 |
| #22590319 | 2 |
| #22590178 | 2 |
| C71×#2178 | 2 |
| #33860 | 71 |