Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 188 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#532 | C2 | semidirect |
| 2. C3×#474 | C2 | semidirect |
| 3. C3×#466 | C2 | semidirect |
| 4. C3×#459 | C2 | semidirect |
| 5. C2×C3×C4⋊C8 | C2 | semidirect |
| 6. #3245 | C3 | direct (N × H) |
| 21. #532 | C2×C3 | semidirect |
| 22. #474 | C2×C3 | semidirect |
| 23. #466 | C2×C3 | semidirect |
| 24. #459 | C2×C3 | semidirect |
| 25. C2×C4⋊C8 | C2×C3 | semidirect |
| 72. C2×C3×C4 | D8 | semidirect |
| 123. C2×C4 | C3×D8 | semidirect |
| 147. C3 | #3245 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C3×#474 | 2 |
| C3×#466 | 2 |
| C3×#459 | 2 |
| C2×C3×C4⋊C8 | 2 |
| #3245 | 3 |