Finite Group DatabasebetaFinite Group Databasebeta← C22×C4⋊((C22⋊C9)⋊C2) #11921389
Order 1152.
2346 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 2346 conjugacy classes of subgroups — too many to draw. Only its 186 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. C23×(C22⋊C9)⋊C2 | C2 | semidirect |
| 2. C22×C4×C22⋊C9 | C2 | semidirect |
| 3. C2×C4⋊((C22⋊C9)⋊C2) | C2 | direct (N × H) |
| 7. C22×(C22⋊C9)⋊C2 | C22 | semidirect |
| 9. C2×C4×C22⋊C9 | C22 | semidirect |
| 10. C4⋊((C22⋊C9)⋊C2) | C22 | direct (N × H) |
| 19. C22×C22⋊C9 | D4 | semidirect |
| 22. C2×(C22⋊C9)⋊C2 | C23 | semidirect |
| 25. C4×C22⋊C9 | C23 | semidirect |
| 49. C2×C22⋊C9 | C2×D4 | semidirect |
| 56. C24×C4 | D9 | semidirect |
| 97. C22⋊C9 | C22×D4 | semidirect |
| 113. C23×C4 | C2×D9 | semidirect |
| 161. C24 | D36 | semidirect |
| 181. C22×C4 | (C22⋊C9)⋊C2 | semidirect |
| 182. C22×C4 | C22×D9 | semidirect |
| 222. C23 | C2×D36 | semidirect |
| 237. C2×C4 | C2×(C22⋊C9)⋊C2 | semidirect |
| 258. C22 | C4⋊((C22⋊C9)⋊C2) | direct (N × H) |
| 259. C22 | C22×D36 | semidirect |
| 263. C4 | C22×(C22⋊C9)⋊C2 | semidirect |
| 269. C2 | C2×C4⋊((C22⋊C9)⋊C2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×(C22⋊C9)⋊C2 | 2 |
| C22×C4×C22⋊C9 | 2 |
| C2×C4⋊((C22⋊C9)⋊C2) | 2 |
| C22×#930 | 3 |
| C22×D36 | 4 |