Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1446 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 236 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. C23×AGL(1,𝔽9) | C2 | semidirect |
| 3. C22×#3777 | C2 | semidirect |
| 4. C2×GO+(4,𝔽2)⋊C4 | C2 | direct (N × H) |
| 10. C22×GO+(4,𝔽2) | C4 | semidirect |
| 13. C22×AGL(1,𝔽9) | C22 | semidirect |
| 15. C2×#3777 | C22 | semidirect |
| 16. GO+(4,𝔽2)⋊C4 | C22 | direct (N × H) |
| 32. C2×GO+(4,𝔽2) | C2×C4 | semidirect |
| 35. C2×AGL(1,𝔽9) | C23 | semidirect |
| 37. #3777 | C23 | semidirect |
| 61. GO+(4,𝔽2) | C22×C4 | semidirect |
| 74. C22×C32 | #102 | semidirect |
| 76. C2×C3⋊D3 | #102 | semidirect |
| 116. C2×C32 | C2×#102 | semidirect |
| 118. C3⋊D3 | C2×#102 | semidirect |
| 157. C32 | C22×#102 | semidirect |
| 198. C22 | GO+(4,𝔽2)⋊C4 | direct (N × H) |
| 209. C2 | C2×GO+(4,𝔽2)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×GO+(4,𝔽2) | 2 |
| C23×AGL(1,𝔽9) | 2 |
| C22×#3777 | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| C22×#102 | 9 |