Finite Group DatabasebetaFinite Group Databasebeta← C22×C4×(C22⋊C9)⋊C2 #11921388
Order 1152.
2346 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 2346 conjugacy classes of subgroups — too many to draw. Only its 226 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 |
|---|---|---|
| 2. C22×C4×C22⋊C9 | C2 | semidirect |
| 3. C22×(C22⋊C9)⋊C4 | C2 | semidirect |
| 4. C2×C4×(C22⋊C9)⋊C2 | C2 | direct (N × H) |
| 7. C22×(C22⋊C9)⋊C2 | C4 | direct (N × H) |
| 10. C2×C4×C22⋊C9 | C22 | semidirect |
| 11. C2×(C22⋊C9)⋊C4 | C22 | semidirect |
| 12. C4×(C22⋊C9)⋊C2 | C22 | direct (N × H) |
| 23. C22×C22⋊C9 | C2×C4 | semidirect |
| 25. C2×(C22⋊C9)⋊C2 | C2×C4 | direct (N × H) |
| 30. C4×C22⋊C9 | C23 | semidirect |
| 31. (C22⋊C9)⋊C4 | C23 | semidirect |
| 60. C2×C22⋊C9 | C22×C4 | semidirect |
| 62. (C22⋊C9)⋊C2 | C22×C4 | direct (N × H) |
| 68. C24×C4 | D9 | semidirect |
| 119. C22⋊C9 | C23×C4 | semidirect |
| 138. C23×C4 | C2×D9 | semidirect |
| 194. C24 | C4×D9 | semidirect |
| 219. C22×C4 | (C22⋊C9)⋊C2 | direct (N × H) |
| 220. C22×C4 | C22×D9 | semidirect |
| 265. C23 | C2×C4×D9 | semidirect |
| 285. C2×C4 | C2×(C22⋊C9)⋊C2 | direct (N × H) |
| 306. C22 | C4×(C22⋊C9)⋊C2 | direct (N × H) |
| 307. C22 | C22×C4×D9 | semidirect |
| 313. C4 | C22×(C22⋊C9)⋊C2 | direct (N × H) |
| 319. 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 |
| C22×(C22⋊C9)⋊C4 | 2 |
| C2×C4×(C22⋊C9)⋊C2 | 2 |
| C22×C4×#67 | 3 |
| C22×C4×D9 | 4 |