Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1067 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1067 conjugacy classes of subgroups — too many to draw. Only its 302 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. C3×Q8×C3⋊C8 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. C4×#3710 | C2 | semidirect |
| 5. #10590256 | C2 | semidirect |
| 23. Q8×C3⋊C8 | D3 | semidirect |
| 29. #3832 | C8 | semidirect |
| 69. C32×Q8 | C2×C8 | semidirect |
| 76. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 79. C4×C3⋊D3 | C2×C8 | semidirect |
| 81. C3×C3⋊C8 | #41 | semidirect |
| 145. C3×Q8 | D3×C8 | semidirect |
| 170. C3⋊C8 | #239 | semidirect |
| 212. C32 | C8×#41 | semidirect |
| 214. Q8 | #3710 | semidirect |
| 246. C3 | C8×#239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3832 | 2 |
| C3×Q8×C3⋊C8 | 2 |
| #10590327 | 2 |
| C4×#3710 | 2 |
| #10590256 | 2 |
| C8×#239 | 3 |