Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#4682 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589139 | C2 | semidirect |
| 21. #4682 | D3 | semidirect |
| 27. C4⋊(C3⋊C16) | D3 | semidirect |
| 37. #3745 | Q8 | semidirect |
| 220. C32 | #2224 | semidirect |
| 257. C3 | #69289 | semidirect |
| 258. C3 | #71387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C3×#4682 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589139 | 2 |
| #10589116 | 2 |
| #71387 | 3 |
| #69289 | 3 |