Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4872 conjugacy classes of subgroups; only the 1801 normal subgroups are shown.
This group has 4872 conjugacy classes of subgroups — too many to draw. Only its 1801 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 |
|---|---|---|
| 4. C2×#64078 | C2 | direct (N × H) |
| 13. #64078 | C22 | direct (N × H) |
| 20. C22×C32×C4 | Q8 | semidirect |
| 42. C2×C32×C4 | C2×Q8 | semidirect |
| 53. C22×C3×C4 | Dic6 | semidirect |
| 63. C22×C32 | C4⋊Q8 | semidirect |
| 68. C32×C4 | C22×Q8 | semidirect |
| 81. C2×C3×C4 | C2×Dic6 | semidirect |
| 88. C2×C32 | C2×C4⋊Q8 | semidirect |
| 96. C22×C4 | #634 | semidirect |
| 102. C22×C3 | #869 | semidirect |
| 106. C3×C4 | C22×Dic6 | semidirect |
| 109. C32 | C22×C4⋊Q8 | semidirect |
| 116. C2×C4 | C2×#634 | semidirect |
| 120. C2×C3 | C2×#869 | semidirect |
| 123. C22 | #64078 | direct (N × H) |
| 128. C4 | C22×#634 | semidirect |
| 130. C3 | C22×#869 | semidirect |
| 131. C2 | C2×#64078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#634 | 2 |
| C22×C32×C42 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C2×#64078 | 2 |
| C22×#869 | 3 |