Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
13209 conjugacy classes of subgroups; only the 7626 normal subgroups are shown.
This group has 13209 conjugacy classes of subgroups — too many to draw. Only its 7626 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. C23×C3×Dic6 | C2 | direct (N × H) |
| 5. C24×Dic6 | C3 | direct (N × H) |
| 9. C22×C3×Dic6 | C22 | direct (N × H) |
| 16. C23×Dic6 | C2×C3 | direct (N × H) |
| 17. C24×C32 | Q8 | semidirect |
| 21. C2×C3×Dic6 | C23 | direct (N × H) |
| 32. C22×Dic6 | C22×C3 | direct (N × H) |
| 33. C23×C32 | C2×Q8 | semidirect |
| 37. C3×Dic6 | C24 | direct (N × H) |
| 43. C24×C3 | Dic6 | direct (N × H) |
| 44. C24×C3 | C3×Q8 | semidirect |
| 53. C2×Dic6 | C23×C3 | direct (N × H) |
| 54. C22×C32 | C22×Q8 | semidirect |
| 64. C23×C3 | C2×Dic6 | direct (N × H) |
| 65. C23×C3 | C2×C3×Q8 | semidirect |
| 74. Dic6 | C24×C3 | direct (N × H) |
| 75. C2×C32 | C23×Q8 | semidirect |
| 77. C24 | C3×Dic6 | direct (N × H) |
| 84. C22×C3 | C22×Dic6 | direct (N × H) |
| 85. C22×C3 | C22×C3×Q8 | semidirect |
| 93. C32 | C24×Q8 | semidirect |
| 94. C23 | C2×C3×Dic6 | direct (N × H) |
| 101. C2×C3 | C23×Dic6 | direct (N × H) |
| 102. C2×C3 | C23×C3×Q8 | semidirect |
| 105. C22 | C22×C3×Dic6 | direct (N × H) |
| 110. C3 | C24×Dic6 | direct (N × H) |
| 111. C3 | C24×C3×Q8 | semidirect |
| 112. C2 | C23×C3×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C4 | 2 |
| C24×C3×Dic3 | 2 |
| C23×C3×Dic6 | 2 |
| C24×C3×Q8 | 3 |
| C24×Dic6 | 3 |