Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
126 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 44 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 | #102 |
| commutator | C2×C8 | C2×C3×C4 |
| Frattini, cosocle | C22×C8 | C22×C3 |
| prime radical | C3×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C22⋊C16 | C2 | semidirect |
| 3. C3×#340 | C2 | semidirect |
| 4. #1347 | C3 | direct (N × H) |
| 5. C2×C3×D8 | C4 | semidirect |
| 10. C3×#107 | C4 | semidirect |
| 13. C22⋊C16 | C2×C3 | semidirect |
| 14. #340 | C2×C3 | semidirect |
| 28. C2×D8 | C3×C4 | semidirect |
| 33. #107 | C3×C4 | semidirect |
| 112. C3 | #1347 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#466 | 2 |
| C3×C22⋊C16 | 2 |
| C3×#340 | 2 |
| #1347 | 3 |