Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10592723 | C2 | semidirect |
| 4. C32×Q8⋊C8 | C2 | semidirect |
| 5. #10589346 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 27. C3×Q8⋊C8 | D3 | semidirect |
| 83. C3⋊(C3⋊C8) | M16 | semidirect |
| 84. C3⋊(C3⋊C8) | SD16 | semidirect |
| 89. Q8⋊C8 | C3⋊D3 | semidirect |
| 191. C32 | #1590 | semidirect |
| 228. C3 | #68224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3755 | 2 |
| #10592723 | 2 |
| #10592537 | 2 |
| C32×Q8⋊C8 | 2 |
| #10589346 | 2 |
| #10589325 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #68224 | 3 |