Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590135 | C2 | semidirect |
| 5. #22589130 | C2 | semidirect |
| 6. #22586444 | C2 | semidirect |
| 7. C71×#2153 | C2 | semidirect |
| 132. #2153 | D71 | semidirect |
| 138. C71 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590135 | 2 |
| C2×#17985813 | 2 |
| #22589250 | 2 |
| #22589130 | 2 |
| #22586444 | 2 |
| C71×#2153 | 2 |
| #13472 | 71 |