Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
379 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 379 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#3746 | C2 | semidirect |
| 4. C3×C4×C3⋊C16 | C2 | semidirect |
| 5. #10589141 | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 21. #63548 | C4 | direct (N × H) |
| 36. C4×C3⋊C16 | D3 | semidirect |
| 47. #3746 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 148. C3⋊C16 | C4×D3 | semidirect |
| 154. C32×C4 | SD32 | semidirect |
| 249. C3×C4 | #800 | semidirect |
| 250. C3×C4 | #827 | semidirect |
| 262. C32 | C4×SD32 | semidirect |
| 297. C4 | #63548 | direct (N × H) |
| 301. C3 | C4×#800 | semidirect |
| 302. C3 | C4×#827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C3×C4×D24 | 2 |
| C2×#63548 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589141 | 2 |
| #10589119 | 2 |
| #10589115 | 2 |
| C4×#827 | 3 |
| C4×#800 | 3 |