Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10592398 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 5. #10589119 | C2 | semidirect |
| 28. C4⋊(C3⋊C16) | D3 | semidirect |
| 135. C32×C4 | SD32 | semidirect |
| 223. C3×C4 | #800 | semidirect |
| 224. C3×C4 | #827 | semidirect |
| 233. C32 | #2208 | semidirect |
| 266. C4 | #63548 | semidirect |
| 270. C3 | #69287 | semidirect |
| 271. C3 | #70892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592398 | 2 |
| C3×C4×D24 | 2 |
| C2×#63548 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589119 | 2 |
| #70892 | 3 |
| #69287 | 3 |