Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
414 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 3. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 4. #10589327 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 125. C32 | #2164 | semidirect |
| 148. C3 | #69883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#405 | 2 |
| #10589415 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589327 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #69883 | 3 |