Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1800 conjugacy classes of subgroups; only the 1065 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 1065 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×#63644 | C2 | direct (N × H) |
| 7. C22×C32×C8 | C4 | semidirect |
| 11. #63644 | C22 | direct (N × H) |
| 22. C2×C32×C8 | C2×C4 | semidirect |
| 29. C22×C3×C8 | Dic3 | semidirect |
| 44. C32×C8 | C22×C4 | semidirect |
| 55. C2×C3×C8 | C2×Dic3 | semidirect |
| 59. C22×C32 | #106 | semidirect |
| 69. C22×C8 | C3⋊Dic3 | semidirect |
| 84. C3×C8 | C22×Dic3 | semidirect |
| 85. C2×C32 | C2×#106 | semidirect |
| 95. C2×C8 | C2×C3⋊Dic3 | semidirect |
| 99. C22×C3 | #817 | semidirect |
| 107. C32 | C22×#106 | semidirect |
| 118. C8 | C22×C3⋊Dic3 | semidirect |
| 119. C2×C3 | C2×#817 | semidirect |
| 122. C22 | #63644 | direct (N × H) |
| 130. C3 | C22×#817 | semidirect |
| 131. C2 | C2×#63644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C8 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| C2×#63644 | 2 |
| C22×#817 | 3 |