Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
696 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 137 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×#63625 | C2 | semidirect |
| 3. C3⋊D3×#107 | C2 | semidirect |
| 4. C32×#357 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 6. #10589369 | C2 | semidirect |
| 7. #10589358 | C2 | semidirect |
| 13. #64121 | C4 | semidirect |
| 26. C3×#357 | D3 | semidirect |
| 39. C32×D8 | C2×C4 | semidirect |
| 47. #3746 | C2×C4 | semidirect |
| 92. #357 | C3⋊D3 | semidirect |
| 102. C3×D8 | C4×D3 | semidirect |
| 178. D8 | C4×C3⋊D3 | semidirect |
| 201. C32 | #2139 | semidirect |
| 239. C3 | #69189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64121 | 2 |
| C2×#63625 | 2 |
| C3⋊D3×#107 | 2 |
| C32×#357 | 2 |
| #10589428 | 2 |
| #10589369 | 2 |
| #10589358 | 2 |
| #69189 | 3 |