Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 177 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. C32×C8×D4 | C2 | semidirect |
| 3. C8×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #10589349 | C2 | semidirect |
| 6. #10589345 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. C3×C8×D4 | D3 | semidirect |
| 42. #3753 | C8 | direct (N × H) |
| 69. C32×D4 | C2×C8 | semidirect |
| 78. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 83. C32×C8 | D8 | semidirect |
| 87. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 90. C8×D4 | C3⋊D3 | semidirect |
| 146. C3×D4 | D3×C8 | semidirect |
| 160. C3×C8 | #213 | semidirect |
| 203. C32 | C8×D8 | semidirect |
| 209. D4 | C8×C3⋊D3 | semidirect |
| 225. C8 | #3753 | direct (N × H) |
| 245. C3 | C8×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×D4 | 2 |
| C4×#3753 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589349 | 2 |
| #10589345 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C8×#213 | 3 |