Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
654 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 98 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. C32×H(3,𝔽4) | C2 | semidirect |
| 2. C3×#5058 | C2 | semidirect |
| 3. C3×#4540 | C2 | semidirect |
| 5. #71948 | C3 | direct (N × H) |
| 11. C3×#874 | C22 | semidirect |
| 12. C3×#803 | C22 | semidirect |
| 14. C3×H(3,𝔽4) | D3 | semidirect |
| 15. C3×H(3,𝔽4) | C2×C3 | semidirect |
| 17. #5058 | C2×C3 | semidirect |
| 19. #4540 | C2×C3 | semidirect |
| 47. #874 | C22×C3 | semidirect |
| 49. #803 | C22×C3 | semidirect |
| 61. H(3,𝔽4) | C3×D3 | semidirect |
| 174. C32 | #1655 | semidirect |
| 202. C3 | #71948 | direct (N × H) |
| 203. C3 | C3×#1655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽4) | 2 |
| C3×#5058 | 2 |
| C3×#4540 | 2 |
| C3×#1655 | 3 |
| #71948 | 3 |