Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2920 conjugacy classes of subgroups; only the 624 normal subgroups are shown.
This group has 2920 conjugacy classes of subgroups — too many to draw. Only its 624 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 |
|---|---|---|
| 1. C2×C3×Q8×A4 | C2 | direct (N × H) |
| 3. C24×C3×Q8 | C3 | semidirect |
| 4. C22×Q8×A4 | C3 | direct (N × H) |
| 7. C3×Q8×A4 | C22 | direct (N × H) |
| 12. C23×C3×Q8 | C2×C3 | semidirect |
| 14. C2×Q8×A4 | C2×C3 | direct (N × H) |
| 16. C22×C3×A4 | Q8 | direct (N × H) |
| 21. C24×Q8 | C32 | semidirect |
| 33. C22×C3×Q8 | A4 | direct (N × H) |
| 34. C22×C3×Q8 | C22×C3 | semidirect |
| 39. Q8×A4 | C22×C3 | direct (N × H) |
| 42. C2×C3×A4 | C2×Q8 | direct (N × H) |
| 49. C23×Q8 | C2×C32 | semidirect |
| 54. C24×C3 | C3×Q8 | semidirect |
| 56. C22×A4 | C3×Q8 | direct (N × H) |
| 65. C2×C3×Q8 | C2×A4 | direct (N × H) |
| 79. C3×A4 | C22×Q8 | direct (N × H) |
| 90. C22×Q8 | C3×A4 | direct (N × H) |
| 91. C22×Q8 | C22×C32 | semidirect |
| 106. C23×C3 | C2×C3×Q8 | semidirect |
| 109. C2×A4 | C2×C3×Q8 | direct (N × H) |
| 114. C3×Q8 | C22×A4 | direct (N × H) |
| 127. C24 | C32×Q8 | semidirect |
| 135. C2×Q8 | C2×C3×A4 | direct (N × H) |
| 156. C22×C3 | Q8×A4 | direct (N × H) |
| 157. C22×C3 | C22×C3×Q8 | semidirect |
| 159. A4 | C22×C3×Q8 | direct (N × H) |
| 173. C23 | C2×C32×Q8 | semidirect |
| 178. Q8 | C22×C3×A4 | direct (N × H) |
| 190. C2×C3 | C2×Q8×A4 | direct (N × H) |
| 201. C22 | C3×Q8×A4 | direct (N × H) |
| 202. C22 | C22×C32×Q8 | semidirect |
| 207. C3 | C22×Q8×A4 | direct (N × H) |
| 211. C2 | C2×C3×Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×A4 | 2 |
| C22×C3×C4×A4 | 2 |
| C24×C3×Q8 | 3 |
| C22×Q8×A4 | 3 |
| C22×C32×Q8 | 4 |