Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C3⋊((C22⋊C9)⋊C2)) #13164472
Order 1728.
1290 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1290 conjugacy classes of subgroups — too many to draw. Only its 139 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×C3⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 2. C2×C3×C4×C22⋊C9 | C2 | semidirect |
| 3. C4⋊(C3⋊((C22⋊C9)⋊C2)) | C2 | direct (N × H) |
| 8. C2×C3⋊((C22⋊C9)⋊C2) | C22 | semidirect |
| 10. C3×C4×C22⋊C9 | C22 | semidirect |
| 19. C2×C4×C22⋊C9 | D3 | semidirect |
| 22. C2×C3×C22⋊C9 | D4 | semidirect |
| 50. C4×C22⋊C9 | C2×D3 | semidirect |
| 54. C3×C22⋊C9 | C2×D4 | semidirect |
| 56. C23×C3×C4 | D9 | semidirect |
| 94. C2×C22⋊C9 | D12 | semidirect |
| 113. C22×C3×C4 | C2×D9 | semidirect |
| 157. C22⋊C9 | C2×D12 | semidirect |
| 161. C23×C4 | C3⋊D9 | semidirect |
| 173. C23×C3 | D36 | semidirect |
| 197. C2×C3×C4 | (C22⋊C9)⋊C2 | semidirect |
| 236. C22×C4 | C2×C3⋊D9 | semidirect |
| 253. C22×C3 | C2×D36 | semidirect |
| 269. C3×C4 | C2×(C22⋊C9)⋊C2 | semidirect |
| 283. C23 | C4⋊(C3⋊D9) | semidirect |
| 297. C2×C4 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 304. C2×C3 | C4⋊((C22⋊C9)⋊C2) | semidirect |
| 322. C22 | C2×C4⋊(C3⋊D9) | semidirect |
| 326. C4 | C2×C3⋊((C22⋊C9)⋊C2) | semidirect |
| 327. C3 | C2×C4⋊((C22⋊C9)⋊C2) | semidirect |
| 333. C2 | C4⋊(C3⋊((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 |
|---|---|
| C22×C3⋊((C22⋊C9)⋊C2) | 2 |
| C2×C3×C4×C22⋊C9 | 2 |
| C4⋊(C3⋊((C22⋊C9)⋊C2)) | 2 |
| C2×#64139 | 3 |
| C2×C4⋊((C22⋊C9)⋊C2) | 3 |
| C2×C4⋊(C3⋊D9) | 4 |