Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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×#14556043 | C2 | semidirect |
| 2. #22586563 | C2 | semidirect |
| 8. C23×D4×C71 | C4 | semidirect |
| 13. C22×C4⋊C4×C71 | C4 | semidirect |
| 14. C22×C22⋊C4×C71 | C4 | semidirect |
| 19. C2×C22⋊Dic71 | D4 | semidirect |
| 137. C2×C4×C71 | #99 | semidirect |
| 183. C71 | #10980 | semidirect |
| 184. C23×D4 | Dic71 | semidirect |
| 189. C22×C4⋊C4 | Dic71 | semidirect |
| 191. C22×C22⋊C4 | Dic71 | semidirect |
| 322. C2×C4 | #14556043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556043 | 2 |
| #22586563 | 2 |
| C22×#121×C71 | 2 |
| #10980 | 71 |