Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
546 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 189 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. #10592711 | C2 | semidirect |
| 3. D4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 6. #10589324 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 71. C32×D4 | M16 | semidirect |
| 87. C3⋊(C3⋊C8) | D8 | semidirect |
| 148. C3×D4 | #208 | semidirect |
| 203. C32 | #1581 | semidirect |
| 209. D4 | #3748 | semidirect |
| 245. C3 | #70879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| #10592711 | 2 |
| D4×C3⋊(C3⋊C8) | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589324 | 2 |
| #10589320 | 2 |
| #70879 | 3 |