Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C42 | C23×C3 |
| socle | C22×C3 | C4×D4 |
| prime radical | C2×C3×D8 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#436 | C2 | semidirect |
| 3. C3×#334 | C2 | semidirect |
| 4. C3×D4⋊C8 | C2 | semidirect |
| 5. C3×#322 | C2 | semidirect |
| 6. #1594 | C3 | direct (N × H) |
| 18. #436 | C2×C3 | semidirect |
| 19. #334 | C2×C3 | semidirect |
| 20. D4⋊C8 | C2×C3 | semidirect |
| 21. #322 | C2×C3 | semidirect |
| 57. C3×C8 | M16 | semidirect |
| 92. C8 | C3×M16 | semidirect |
| 106. C3 | #1594 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| C3×#436 | 2 |
| C3×#334 | 2 |
| C3×D4⋊C8 | 2 |
| C3×#322 | 2 |
| #1594 | 3 |