Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3054 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 3054 conjugacy classes of subgroups — too many to draw. Only its 393 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. C2×C32×H(5,𝔽2) | C2 | semidirect |
| 2. C2×#64146 | C2 | semidirect |
| 3. #10592943 | C2 | direct (N × H) |
| 4. C2×#63661 | C2 | semidirect |
| 6. C24×C3⋊D3 | C22 | semidirect |
| 8. C32×H(5,𝔽2) | C22 | semidirect |
| 13. C2×#3757 | C22 | semidirect |
| 15. #64146 | C22 | semidirect |
| 17. #63661 | C22 | semidirect |
| 18. C2×C3×H(5,𝔽2) | D3 | semidirect |
| 23. C24×C32 | D4 | semidirect |
| 28. C23×C3⋊D3 | C23 | semidirect |
| 37. C2×C32×D4 | D4 | semidirect |
| 40. C22×C32×C4 | D4 | semidirect |
| 45. #3757 | C23 | semidirect |
| 50. C3×H(5,𝔽2) | C2×D3 | semidirect |
| 68. C23×C32 | C2×D4 | semidirect |
| 84. C2×C32×C4 | C2×D4 | semidirect |
| 88. C2×H(5,𝔽2) | C3⋊D3 | semidirect |
| 93. C24×C3 | #67 | semidirect |
| 107. C2×C3×D4 | #67 | semidirect |
| 110. C22×C3×C4 | #67 | semidirect |
| 137. H(5,𝔽2) | C2×C3⋊D3 | semidirect |
| 155. C23×C3 | C2×#67 | semidirect |
| 171. C2×C3×C4 | C2×#67 | semidirect |
| 178. C2×C32 | B(4,𝔽2) | semidirect |
| 186. C24 | #638 | semidirect |
| 198. C2×D4 | #638 | semidirect |
| 202. C22×C4 | #638 | semidirect |
| 224. C32 | C2×B(4,𝔽2) | semidirect |
| 240. C23 | C2×#638 | semidirect |
| 252. C2×C4 | C2×#638 | semidirect |
| 256. C2×C3 | #5244 | semidirect |
| 277. C3 | C2×#5244 | semidirect |
| 282. C2 | #10592943 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×H(5,𝔽2) | 2 |
| C2×#64146 | 2 |
| #10592943 | 2 |
| C2×#63661 | 2 |
| C2×#5244 | 3 |