Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×D3 |
| commutator, socle, prime radical, cosocle | C23×C3 | C24 |
| Frattini | C23 | C23×D3 |
| Fitting | C3×C4×C4⋊C4 | C2 |
| hypercenter | C4×C4⋊C4 | D3 |
| hypocenter | C3 | #2399 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 56. C3×C42 | Q8 | semidirect |
| 65. C4×Dic3 | Q8 | semidirect |
| 138. C42 | Dic6 | semidirect |
| 199. C3 | #2399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C3×C4×C4⋊C4 | 2 |
| #4982 | 2 |
| #4979 | 2 |
| C4×C4⋊Dic3 | 2 |
| #4932 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4657 | 2 |
| #4656 | 2 |
| #2399 | 3 |