Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 1. #22599526 | C2 | semidirect |
| 3. #22593501 | C2 | semidirect |
| 4. #22586941 | C2 | semidirect |
| 5. #22586784 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 7. C71×#1980 | C2 | semidirect |
| 220. #1980 | D71 | semidirect |
| 224. C71 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599526 | 2 |
| #22598427 | 2 |
| #22593501 | 2 |
| #22586941 | 2 |
| #22586784 | 2 |
| #22586196 | 2 |
| C71×#1980 | 2 |
| #10005 | 71 |