Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3606 conjugacy classes of subgroups; only the 855 normal subgroups are shown.
This group has 3606 conjugacy classes of subgroups — too many to draw. Only its 855 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×Q82 | C2 |
| hypercenter | Q82 | C3⋊D3 |
| hypocenter | C32 | #3483 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×Q82 | C2 | semidirect |
| 2. #10596205 | C2 | semidirect |
| 3. #10596196 | C2 | semidirect |
| 4. #10596048 | C2 | semidirect |
| 5. C4×#3832 | C2 | semidirect |
| 19. C3×Q82 | D3 | semidirect |
| 53. C32×Q8 | #41 | semidirect |
| 62. Q82 | C3⋊D3 | semidirect |
| 102. C3×Q8 | #239 | semidirect |
| 135. C32 | #3483 | semidirect |
| 138. Q8 | #3832 | semidirect |
| 157. C3 | #87040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q82 | 2 |
| #10596205 | 2 |
| #10596196 | 2 |
| #10596048 | 2 |
| C4×#3832 | 2 |
| #87040 | 3 |