Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10596542 | C2 | semidirect |
| 3. C2×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. #10596416 | C2 | semidirect |
| 5. #10596410 | C2 | semidirect |
| 6. #10596409 | C2 | semidirect |
| 7. PSU(3,𝔽2)⋊Q8 | C2 | semidirect |
| 8. GO+(4,𝔽2)⋊Q8 | C2 | semidirect |
| 87. C2×C32×C4 | SD16 | semidirect |
| 88. C2×C3⋊Dic3 | SD16 | semidirect |
| 89. C4×C3⋊D3 | SD16 | semidirect |
| 90. C4×C3⋊D3 | SD16 | semidirect |
| 243. C32 | #3246 | semidirect |
| 275. C2×C4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596542 | 2 |
| #10596511 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| #10596416 | 2 |
| #10596410 | 2 |
| #10596409 | 2 |
| PSU(3,𝔽2)⋊Q8 | 2 |
| GO+(4,𝔽2)⋊Q8 | 2 |
| #3246 | 9 |