Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22588771 | C2 | semidirect |
| 4. #22588544 | C2 | semidirect |
| 6. #22586705 | C2 | semidirect |
| 7. C71×#1305 | C2 | semidirect |
| 221. #1305 | D71 | semidirect |
| 222. C71 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599147 | 2 |
| #22588801 | 2 |
| #22588771 | 2 |
| #22588544 | 2 |
| #22586907 | 2 |
| #22586705 | 2 |
| C71×#1305 | 2 |
| #10562 | 71 |