Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
510 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 105 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×#509 | C2 | semidirect |
| 2. #10592895 | C2 | semidirect |
| 3. #10592892 | C2 | semidirect |
| 4. #10592850 | C2 | semidirect |
| 5. #10589429 | C2 | semidirect |
| 6. #10589382 | C2 | semidirect |
| 7. #10589377 | C2 | semidirect |
| 24. C3×#509 | D3 | semidirect |
| 35. C32×Q16 | D4 | semidirect |
| 39. C32×D8 | D4 | semidirect |
| 87. #509 | C3⋊D3 | semidirect |
| 97. C3×Q16 | #67 | semidirect |
| 101. C3×D8 | #67 | semidirect |
| 166. Q16 | #638 | semidirect |
| 174. D8 | #638 | semidirect |
| 193. C32 | #2213 | semidirect |
| 227. C3 | #71514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#509 | 2 |
| #10592895 | 2 |
| #10592892 | 2 |
| #10592850 | 2 |
| #10589429 | 2 |
| #10589382 | 2 |
| #10589377 | 2 |
| #71514 | 3 |