Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
377 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 377 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C3×D3×C16 | C2 | semidirect |
| 3. C16×C3⋊Dic3 | C2 | semidirect |
| 4. #10589133 | C2 | semidirect |
| 5. (C2×D3)⋊(C3⋊C16) | C2 | semidirect |
| 18. C2×D3×C16 | D3 | semidirect |
| 34. C32×C16 | D4 | semidirect |
| 61. #625 | C16 | direct (N × H) |
| 91. C3×C16 | #67 | semidirect |
| 98. C2×C3×D3 | C2×C16 | semidirect |
| 102. C3⋊Dic3 | C2×C16 | semidirect |
| 152. C16 | #625 | direct (N × H) |
| 160. C2×D3 | D3×C16 | semidirect |
| 171. C32 | D4×C16 | semidirect |
| 202. C3 | C16×#67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C16 | 2 |
| C8×#625 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589133 | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| C16×#67 | 3 |