Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D3 |
| commutator, socle | C22×C3 | C2×C42 |
| Fitting | C3×#431 | C2 |
| prime radical | C23×C3 | C42 |
| cosocle | C3×C42 | C23 |
| hypercenter | #431 | D3 |
| hypocenter | C3 | #1452 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4455 | C2 | semidirect |
| 5. #4454 | C2 | semidirect |
| 110. C3 | #1452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#431 | 2 |
| #4925 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4455 | 2 |
| #4454 | 2 |
| #1452 | 3 |