Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2520 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 2520 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 | C32×#376 | C2 |
| hypercenter | #376 | C3⋊D3 |
| hypocenter | C32 | #2397 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C32×#376 | C2 | semidirect |
| 3. #10592376 | C2 | semidirect |
| 4. #10592370 | C2 | semidirect |
| 14. C3×#376 | D3 | semidirect |
| 24. C32×C42 | D4 | semidirect |
| 48. #376 | C3⋊D3 | semidirect |
| 56. C3×C42 | D12 | semidirect |
| 96. C42 | C4⋊(C3⋊D3) | semidirect |
| 105. C32 | #2397 | semidirect |
| 127. C3 | #73418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C32×#376 | 2 |
| #10592376 | 2 |
| #10592370 | 2 |
| #73418 | 3 |