Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
618 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| socle | C22×C3 | C2×C22⋊C4 |
| prime radical | C22×C3×#41 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#104 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. C3×C4×C22⋊C4 | C2 | semidirect |
| 5. #1789 | C3 | direct (N × H) |
| 9. C2×C3×#41 | C4 | semidirect |
| 11. C22×C3×Q8 | C4 | semidirect |
| 13. C22×C3×D4 | C4 | semidirect |
| 16. C2×C3×M16 | C22 | semidirect |
| 18. C2×C3×C42 | C22 | semidirect |
| 24. C2×#104 | C2×C3 | semidirect |
| 25. #407 | C2×C3 | semidirect |
| 26. C4×C22⋊C4 | C2×C3 | semidirect |
| 63. C2×#41 | C3×C4 | semidirect |
| 65. C22×Q8 | C3×C4 | semidirect |
| 67. C22×D4 | C3×C4 | semidirect |
| 70. C2×M16 | C22×C3 | semidirect |
| 72. C2×C42 | C22×C3 | semidirect |
| 89. C3×Q8 | C22⋊C4 | semidirect |
| 94. C3×D4 | C22⋊C4 | semidirect |
| 158. C22×C3 | #104 | semidirect |
| 179. Q8 | C3×C22⋊C4 | semidirect |
| 184. D4 | C3×C22⋊C4 | semidirect |
| 222. C22 | C3×#104 | semidirect |
| 231. C3 | #1789 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×C3×#104 | 2 |
| C3×#407 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #1789 | 3 |