Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
355 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#63543 | C2 | semidirect |
| 3. C2×D3×C3⋊C16 | C2 | semidirect |
| 4. #10589368 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 7. #10589133 | C2 | semidirect |
| 31. (C2×D3)⋊C16 | D3 | semidirect |
| 32. (C2×D3)⋊C16 | D3 | semidirect |
| 54. C3⋊(C3⋊C16) | D4 | semidirect |
| 160. C2×C3×D3 | M32 | semidirect |
| 258. C2×D3 | #798 | semidirect |
| 275. C32 | #2168 | semidirect |
| 320. C3 | #69102 | semidirect |
| 321. C3 | #69103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#625 | 2 |
| C2×#63543 | 2 |
| C2×D3×C3⋊C16 | 2 |
| #10589368 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| #10589133 | 2 |
| #69103 | 3 |
| #69102 | 3 |