Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
303 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D32 |
| commutator, socle, prime radical | C22×C32 | C22×C8 |
| Fitting | C32×C4×C8 | C22 |
| cosocle | C2×C32×C8 | C23 |
| hypercenter | C4×C8 | D32 |
| hypocenter | C32 | #2183 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 37. C3×C3⋊C16 | Q8 | semidirect |
| 104. C3⋊C16 | Dic6 | semidirect |
| 185. C32 | #2183 | semidirect |
| 213. C3 | #69048 | semidirect |
| 214. C3 | #69281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589133 | 2 |
| #10589104 | 2 |
| #69281 | 3 |
| #69048 | 3 |