Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
550 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 91 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. C23×AGL(1,𝔽9) | C2 | semidirect |
| 3. C2×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. C2×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. #10593267 | C2 | semidirect |
| 41. C2×AGL(1,𝔽9) | D4 | semidirect |
| 42. C2×C32×D4 | C8 | semidirect |
| 43. C2×#638 | C8 | semidirect |
| 44. C2×#638 | C8 | semidirect |
| 47. C2×C4⋊(C3⋊D3) | C8 | semidirect |
| 57. C23×C32 | C2×C8 | semidirect |
| 66. C22×C3⋊D3 | C2×C8 | semidirect |
| 88. C2×C32×C4 | C2×C8 | semidirect |
| 91. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 112. C22×C32 | C22⋊C8 | semidirect |
| 123. C2×C3⋊D3 | C22⋊C8 | semidirect |
| 188. C2×D4 | AGL(1,𝔽9) | semidirect |
| 235. C32 | #1869 | semidirect |
| 248. C23 | C2×AGL(1,𝔽9) | semidirect |
| 272. C2×C4 | C2×AGL(1,𝔽9) | semidirect |
| 301. C22 | C22⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽9) | 2 |
| C2×D4×#157 | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| #10593267 | 2 |
| #1869 | 9 |