Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#4696 | C2 | semidirect |
| 2. C3×C4×D24 | C2 | semidirect |
| 3. C2×#63547 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 6. #10589117 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 29. #4696 | D3 | semidirect |
| 30. C4×D24 | D3 | semidirect |
| 279. C32 | #2210 | semidirect |
| 324. C3 | #70890 | semidirect |
| 325. C3 | #71323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| C3×C4×D24 | 2 |
| C2×#63547 | 2 |
| C2×#63545 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589117 | 2 |
| #10589114 | 2 |
| #71323 | 3 |
| #70890 | 3 |