Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×C32×SD32 | C2 | semidirect |
| 2. Q16×C3⋊Dic3 | C2 | semidirect |
| 3. C2×#63655 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 6. #10589375 | C2 | semidirect |
| 7. #10589367 | C2 | semidirect |
| 22. C2×C3×SD32 | D3 | semidirect |
| 35. C32×Q16 | D4 | semidirect |
| 82. C2×SD32 | C3⋊D3 | semidirect |
| 94. C3×Q16 | #67 | semidirect |
| 120. C3⋊Dic3 | SD32 | semidirect |
| 163. Q16 | #638 | semidirect |
| 190. C32 | #2207 | semidirect |
| 227. C3 | #71475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| Q16×C3⋊Dic3 | 2 |
| C2×#63655 | 2 |
| #10592850 | 2 |
| #10589428 | 2 |
| #10589375 | 2 |
| #10589367 | 2 |
| #71475 | 3 |