Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
544 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10593951 | C2 | semidirect |
| 2. #10592774 | C2 | semidirect |
| 3. C3×#5075 | C2 | semidirect |
| 5. #10589090 | C2 | semidirect |
| 6. #10589085 | C2 | semidirect |
| 7. #10589084 | C2 | semidirect |
| 34. #5075 | D3 | semidirect |
| 375. C32 | #1620 | semidirect |
| 434. C3 | #71031 | semidirect |
| 435. C3 | #71284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593951 | 2 |
| #10592774 | 2 |
| C3×#5075 | 2 |
| C3×#5073 | 2 |
| #10589090 | 2 |
| #10589085 | 2 |
| #10589084 | 2 |
| #71284 | 3 |
| #71031 | 3 |