Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22588773 | C2 | semidirect |
| 5. #22586703 | C2 | semidirect |
| 6. #22586245 | C2 | semidirect |
| 7. C71×#1855 | C2 | semidirect |
| 218. #1855 | 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 |
| #22588803 | 2 |
| #22588773 | 2 |
| #22586909 | 2 |
| #22586703 | 2 |
| #22586245 | 2 |
| C71×#1855 | 2 |
| #10562 | 71 |