Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22586627 | C2 | semidirect |
| 5. #22586621 | C2 | semidirect |
| 6. #22586229 | C2 | semidirect |
| 7. C71×#1299 | C2 | semidirect |
| 154. #1299 | D71 | semidirect |
| 155. C71 | #8245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597051 | 2 |
| #22587000 | 2 |
| #22586931 | 2 |
| #22586627 | 2 |
| #22586621 | 2 |
| #22586229 | 2 |
| C71×#1299 | 2 |
| #8245 | 71 |