Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 147 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×#446 | C2 | semidirect |
| 4. #10589401 | C2 | semidirect |
| 6. #10589345 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 24. C3×#446 | D3 | semidirect |
| 85. #446 | C3⋊D3 | semidirect |
| 191. C32 | #1585 | semidirect |
| 228. C3 | #70954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#446 | 2 |
| C4×#3755 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10589401 | 2 |
| #10589349 | 2 |
| #10589345 | 2 |
| #10589320 | 2 |
| #70954 | 3 |