Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C3⋊(#41⋊C3)) #11923178
Order 1152.
857 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 857 conjugacy classes of subgroups — too many to draw. Only its 119 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⋊(#41⋊C3) | C2 | semidirect |
| 2. C2×C3×C4×SL(2,𝔽3) | C2 | semidirect |
| 3. C4⋊(C3⋊(#41⋊C3)) | C2 | direct (N × H) |
| 4. C2×#5577 | C3 | semidirect |
| 8. C2×C3⋊(#41⋊C3) | C22 | semidirect |
| 10. C3×C4×SL(2,𝔽3) | C22 | semidirect |
| 15. #5577 | C2×C3 | semidirect |
| 21. C2×C4×SL(2,𝔽3) | D3 | semidirect |
| 24. C2×C3×SL(2,𝔽3) | D4 | semidirect |
| 56. C4×SL(2,𝔽3) | C2×D3 | semidirect |
| 62. C3×SL(2,𝔽3) | C2×D4 | semidirect |
| 101. C2×SL(2,𝔽3) | D12 | semidirect |
| 160. C2×C3×C4 | #41⋊C3 | semidirect |
| 173. SL(2,𝔽3) | C2×D12 | semidirect |
| 232. C3×C4 | C2×#41⋊C3 | semidirect |
| 260. C2×C4 | C3⋊(#41⋊C3) | semidirect |
| 270. C2×C3 | C4⋊(#41⋊C3) | semidirect |
| 288. C4 | C2×C3⋊(#41⋊C3) | semidirect |
| 291. C3 | C2×C4⋊(#41⋊C3) | semidirect |
| 293. C2 | C4⋊(C3⋊(#41⋊C3)) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(#41⋊C3) | 2 |
| C2×C3×C4×SL(2,𝔽3) | 2 |
| C4⋊(C3⋊(#41⋊C3)) | 2 |
| C2×#5577 | 3 |
| C2×C4⋊(#41⋊C3) | 3 |
| C2×C3×C4⋊Dic3 | 4 |