Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D3 |
| commutator, socle, prime radical | C23×C3 | C22×C4 |
| Fitting | C3×#336 | C2 |
| cosocle | C22×C3×C4 | C23 |
| hypercenter | #336 | D3 |
| hypocenter | C3 | #1840 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 117. C3 | #1840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4932 | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| #1840 | 3 |