Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
485 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C3×Dic12 | C2 | semidirect |
| 3. C2×C3×#800 | C2 | semidirect |
| 4. C32×C22⋊C16 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 7. #69112 | C3 | direct (N × H) |
| 20. C22×Dic12 | C2×C3 | semidirect |
| 24. C2×#800 | C2×C3 | semidirect |
| 27. C3×C22⋊C16 | D3 | semidirect |
| 28. C3×C22⋊C16 | C2×C3 | semidirect |
| 29. #4503 | C2×C3 | semidirect |
| 45. C3×Dic12 | D4 | semidirect |
| 94. C22⋊C16 | C3×D3 | semidirect |
| 131. Dic12 | C3×D4 | semidirect |
| 138. C22×C32 | SD32 | semidirect |
| 234. C22×C3 | #800 | semidirect |
| 235. C22×C3 | C3×SD32 | semidirect |
| 254. C32 | #2185 | semidirect |
| 291. C22 | C3×#800 | semidirect |
| 299. C3 | #69112 | direct (N × H) |
| 300. C3 | C3×#2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic12 | 2 |
| C3×#5115 | 2 |
| C2×C3×#800 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2185 | 3 |
| #69112 | 3 |