Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2832 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 2832 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Frattini | C23 | C23×C3⋊D3 |
| Fitting | C22×C32×#41 | C2 |
| hypercenter | C22×#41 | C3⋊D3 |
| hypocenter | C32 | #2388 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×#41 | C2 | semidirect |
| 2. C2×C4×#638 | C2 | semidirect |
| 3. #10592930 | C2 | semidirect |
| 4. #10592929 | C2 | semidirect |
| 5. #10592922 | C2 | semidirect |
| 6. #10592921 | C2 | semidirect |
| 7. C4×#3757 | C2 | semidirect |
| 23. C22×C3×#41 | D3 | semidirect |
| 37. C22×C32×C4 | D4 | semidirect |
| 75. C22×C3⋊D3 | #41 | semidirect |
| 88. C2×C3⋊Dic3 | #41 | semidirect |
| 90. C22×#41 | C3⋊D3 | semidirect |
| 104. C22×C3×C4 | #67 | semidirect |
| 191. C22×C4 | #638 | semidirect |
| 215. C32 | #2388 | semidirect |
| 260. C3 | #84095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×#41 | 2 |
| C2×C4×#638 | 2 |
| #10592930 | 2 |
| #10592929 | 2 |
| #10592922 | 2 |
| #10592921 | 2 |
| C4×#3757 | 2 |
| #84095 | 3 |