Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22588464 | C2 | semidirect |
| 5. #22586446 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C71×#2153 | C2 | semidirect |
| 10. #17986112 | C4 | semidirect |
| 11. #17986107 | C4 | semidirect |
| 152. #2153 | D71 | semidirect |
| 158. C71 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597225 | 2 |
| #22590077 | 2 |
| #22590069 | 2 |
| #22588464 | 2 |
| #22586446 | 2 |
| #22586439 | 2 |
| C71×#2153 | 2 |
| #12828 | 71 |