Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×#826 |
| commutator, cosocle | C32×C16 | C23 |
| Frattini | C16 | C2×D32 |
| Fitting | C32×Q32 | C22 |
| socle | C2×C32 | C2×D16 |
| hypercenter | Q32 | D32 |
| hypocenter | C32 | #2263 |
| LCS | G ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#4919 | C2 | semidirect |
| 2. D3×D48 | C2 | semidirect |
| 3. #10589387 | C2 | semidirect |
| 4. C3×#4521 | C2 | semidirect |
| 5. #10589071 | C2 | semidirect |
| 6. #10589070 | C2 | semidirect |
| 7. #10589068 | C2 | semidirect |
| 12. C32×Q32 | C22 | semidirect |
| 16. C3×D48 | C22 | semidirect |
| 19. C3⋊(C3⋊C32) | C22 | semidirect |
| 20. C3×C3⋊C32 | C22 | semidirect |
| 22. #4919 | D3 | semidirect |
| 29. #4521 | D3 | semidirect |
| 53. C3×Q32 | C2×D3 | semidirect |
| 54. C3×Q32 | C2×D3 | semidirect |
| 66. D48 | C2×D3 | semidirect |
| 72. C3⋊C32 | C2×D3 | semidirect |
| 126. Q32 | D32 | semidirect |
| 195. C32 | #2263 | semidirect |
| 228. C3 | #69380 | semidirect |
| 229. C3 | #71509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4919 | 2 |
| D3×D48 | 2 |
| #10589387 | 2 |
| C3×#4521 | 2 |
| #10589071 | 2 |
| #10589070 | 2 |
| #10589068 | 2 |
| #71509 | 3 |
| #69380 | 3 |