Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#14556074 | C2 | semidirect |
| 4. C2×#17985816 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#2141 | C2 | semidirect |
| 193. #2141 | D71 | semidirect |
| 196. C71 | #13322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556074 | 2 |
| C2×#17986271 | 2 |
| #22597996 | 2 |
| C2×#17985816 | 2 |
| C2×#17985784 | 2 |
| #22586435 | 2 |
| C71×#2141 | 2 |
| #13322 | 71 |