Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×#4679 | C2 | semidirect |
| 4. #10589320 | C2 | semidirect |
| 5. #10589100 | C2 | semidirect |
| 6. #10589083 | C2 | semidirect |
| 30. #4679 | D3 | semidirect |
| 109. C3⋊(C3⋊C8) | M16 | semidirect |
| 288. C32 | #1592 | semidirect |
| 333. C3 | #70860 | semidirect |
| 334. C3 | #70955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4688 | 2 |
| C3×#4679 | 2 |
| C4×#3715 | 2 |
| #10589320 | 2 |
| #10589100 | 2 |
| #10589083 | 2 |
| #10589080 | 2 |
| #70955 | 3 |
| #70860 | 3 |