Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×C22⋊C4 |
| commutator | C23 | C22×C3×C4 |
| Frattini, cosocle | C24 | C23×C3 |
| prime radical | C2×C3×#121 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#99 | C2 | semidirect |
| 3. C3×#380 | C2 | semidirect |
| 4. C3×C4×C22⋊C4 | C2 | semidirect |
| 5. #1964 | C3 | direct (N × H) |
| 6. C22×C3×D4 | C4 | semidirect |
| 14. C2×C3×C4⋊C4 | C4 | semidirect |
| 15. C2×C3×C22⋊C4 | C4 | semidirect |
| 23. C2×#99 | C2×C3 | semidirect |
| 24. #380 | C2×C3 | semidirect |
| 25. C4×C22⋊C4 | C2×C3 | semidirect |
| 52. C3×C22⋊C4 | D4 | semidirect |
| 54. C22×D4 | C3×C4 | semidirect |
| 62. C2×C4⋊C4 | C3×C4 | semidirect |
| 63. C2×C22⋊C4 | C3×C4 | semidirect |
| 130. C22⋊C4 | C3×D4 | semidirect |
| 155. C3×C4 | #99 | semidirect |
| 221. C4 | C3×#99 | semidirect |
| 222. C3 | #1964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#121 | 2 |
| C2×C3×#99 | 2 |
| C3×#380 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #1964 | 3 |