Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1369 conjugacy classes of subgroups; only the 596 normal subgroups are shown.
This group has 1369 conjugacy classes of subgroups — too many to draw. Only its 596 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 |
|---|---|---|
| 3. C2×#63576 | C2 | direct (N × H) |
| 7. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 11. #63576 | C22 | direct (N × H) |
| 24. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 53. C3⋊(C3⋊C8) | C22×C4 | semidirect |
| 79. C22×C32 | #107 | semidirect |
| 119. C2×C32 | C2×#107 | semidirect |
| 139. C22×C3 | #807 | semidirect |
| 152. C32 | C22×#107 | semidirect |
| 169. C2×C3 | C2×#807 | semidirect |
| 173. C22 | #63576 | direct (N × H) |
| 183. C3 | C22×#807 | semidirect |
| 184. C2 | C2×#63576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C3⋊C8) | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| C2×#63576 | 2 |
| C22×#807 | 3 |