Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 2. D4×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #10589324 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. C32×D8 | C8 | semidirect |
| 48. C32×D4 | C2×C8 | semidirect |
| 56. C32×C8 | C2×C8 | semidirect |
| 60. C3⋊(C3⋊C8) | D8 | direct (N × H) |
| 68. C3×D8 | C3⋊C8 | semidirect |
| 101. C3×D4 | C2×C3⋊C8 | semidirect |
| 109. C3×C8 | C2×C3⋊C8 | semidirect |
| 120. D8 | C3⋊(C3⋊C8) | direct (N × H) |
| 141. C32 | C8×D8 | semidirect |
| 144. D4 | C2×C3⋊(C3⋊C8) | semidirect |
| 156. C8 | C2×C3⋊(C3⋊C8) | semidirect |
| 171. C3 | D8×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| D4×C3⋊(C3⋊C8) | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589324 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| D8×C3⋊C8 | 3 |