Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1088 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 317 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D3 |
| commutator | C22×C3 | C2×C42 |
| Fitting | C24×C3×C4 | C2 |
| socle, cosocle | C24×C3 | C23 |
| prime radical | C25×C3 | C22 |
| hypercenter | C24×C4 | D3 |
| hypocenter | C3 | C22⋊#95 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3⋊#95 | C2 | semidirect |
| 8. C23×C3×C4 | C4 | semidirect |
| 13. C2×#217 | C4 | semidirect |
| 37. C22×Dic3 | C2×C4 | semidirect |
| 43. C23×C4 | Dic3 | semidirect |
| 72. C2×C3×C4 | C22⋊C4 | semidirect |
| 105. C22×C3 | #95 | semidirect |
| 148. C2×C4 | #217 | semidirect |
| 163. C22 | C3⋊#95 | semidirect |
| 178. C3 | C22⋊#95 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C22×#217 | 2 |
| C2×C3⋊#95 | 2 |
| C22⋊#95 | 3 |