Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
430 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10592786 | C2 | semidirect |
| 2. C3×#5085 | C2 | semidirect |
| 4. #10590327 | C2 | semidirect |
| 5. C3×#4547 | C2 | semidirect |
| 6. #10589097 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 29. #5085 | D3 | semidirect |
| 35. #4547 | D3 | semidirect |
| 106. C4⋊(C3⋊D3) | SD16 | semidirect |
| 118. C3×C3⋊C8 | D8 | semidirect |
| 262. C3⋊C8 | #213 | semidirect |
| 327. C32 | #1665 | semidirect |
| 380. C3 | #68440 | semidirect |
| 381. C3 | #71267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592786 | 2 |
| C3×#5085 | 2 |
| #10590355 | 2 |
| #10590327 | 2 |
| C3×#4547 | 2 |
| #10589097 | 2 |
| #10589090 | 2 |
| #71267 | 3 |
| #68440 | 3 |