Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1272 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 537 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. #10592379 | C2 | direct (N × H) |
| 24. C2×C32×C8 | Q8 | semidirect |
| 50. C32×C8 | C2×Q8 | semidirect |
| 60. C2×C3×C8 | Dic6 | semidirect |
| 92. C3×C8 | C2×Dic6 | semidirect |
| 93. C2×C32 | #498 | semidirect |
| 101. C2×C8 | #634 | semidirect |
| 115. C32 | C2×#498 | semidirect |
| 125. C8 | C2×#634 | semidirect |
| 126. C2×C3 | #4680 | semidirect |
| 136. C3 | C2×#4680 | semidirect |
| 137. C2 | #10592379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C2×C32×C4×C8 | 2 |
| C2×#63644 | 2 |
| #10592379 | 2 |
| C2×#4680 | 3 |