Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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×#63639 | C2 | semidirect |
| 3. C2×C16×C3⋊D3 | C2 | semidirect |
| 4. C32×C22⋊C16 | C2 | semidirect |
| 5. #10589373 | C2 | semidirect |
| 6. #10589368 | C2 | semidirect |
| 7. #10589367 | C2 | semidirect |
| 25. C3×C22⋊C16 | D3 | semidirect |
| 47. C3⋊(C3⋊C16) | D4 | semidirect |
| 84. C22⋊C16 | C3⋊D3 | semidirect |
| 111. C2×C3⋊D3 | M32 | semidirect |
| 185. C32 | #2168 | semidirect |
| 221. C3 | #69103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#638 | 2 |
| C2×#63639 | 2 |
| C2×C16×C3⋊D3 | 2 |
| C32×C22⋊C16 | 2 |
| #10589373 | 2 |
| #10589368 | 2 |
| #10589367 | 2 |
| #69103 | 3 |