Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
534 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #22593729 | C2 | semidirect |
| 5. #22586788 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 7. C71×#1528 | C2 | semidirect |
| 206. #1528 | D71 | semidirect |
| 209. C71 | #10007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599530 | 2 |
| #22598463 | 2 |
| #22593729 | 2 |
| #22589259 | 2 |
| #22586788 | 2 |
| #22586195 | 2 |
| C71×#1528 | 2 |
| #10007 | 71 |