Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #121 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C22×C3×D8 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#108 | C2 | semidirect |
| 3. C3×#418 | C2 | semidirect |
| 4. C2×C3×#100 | C2 | semidirect |
| 5. C3×#405 | C2 | semidirect |
| 6. #1978 | C3 | direct (N × H) |
| 11. C2×C3×D8 | C4 | semidirect |
| 22. C2×#108 | C2×C3 | semidirect |
| 23. #418 | C2×C3 | semidirect |
| 24. C2×#100 | C2×C3 | semidirect |
| 25. #405 | C2×C3 | semidirect |
| 53. C2×D8 | C3×C4 | semidirect |
| 157. C3 | #1978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×C3×#108 | 2 |
| C3×#418 | 2 |
| C2×C3×#100 | 2 |
| C3×#405 | 2 |
| #1978 | 3 |