Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 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×Q8 | C2 | semidirect |
| 4. #10589401 | C2 | semidirect |
| 6. #10589346 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 24. C3×C8×Q8 | D3 | semidirect |
| 41. #3755 | C8 | direct (N × H) |
| 67. C32×Q8 | C2×C8 | semidirect |
| 80. C32×C8 | SD16 | semidirect |
| 84. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 85. C8×Q8 | C3⋊D3 | semidirect |
| 139. C3×Q8 | D3×C8 | semidirect |
| 152. C3×C8 | #215 | semidirect |
| 191. C32 | C8×SD16 | semidirect |
| 194. Q8 | C8×C3⋊D3 | semidirect |
| 211. C8 | #3755 | direct (N × H) |
| 228. C3 | C8×#215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| C4×#3755 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10589401 | 2 |
| #10589349 | 2 |
| #10589346 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C8×#215 | 3 |