Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22586453 | C2 | semidirect |
| 5. #22586451 | C2 | semidirect |
| 6. #22586434 | C2 | semidirect |
| 7. C71×#1381 | C2 | semidirect |
| 142. #1381 | D71 | semidirect |
| 143. C71 | #12878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596948 | 2 |
| #22589953 | 2 |
| #22588387 | 2 |
| #22586453 | 2 |
| #22586451 | 2 |
| #22586434 | 2 |
| C71×#1381 | 2 |
| #12878 | 71 |