Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
506 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#157 |
| commutator | C2×C32 | C43 |
| Fitting | C32×#95 | C4 |
| socle, prime radical | C23×C32 | C22×C4 |
| cosocle | C22×C3⋊Dic3 | C23 |
| hypercenter | #95 | #157 |
| hypocenter | C32 | #1726 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #63777 | C4 | semidirect |
| 8. C4×#622 | C4 | semidirect |
| 82. C32 | #1726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63777 | 2 |
| C2×C4×#622 | 2 |
| #10592347 | 2 |
| #1726 | 9 |