Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 168 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 ◁ C3×#117 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#540 | C2 | semidirect |
| 2. C3×#478 | C2 | semidirect |
| 3. C3×#469 | C2 | semidirect |
| 4. C3×#466 | C2 | semidirect |
| 5. C3×#459 | C2 | semidirect |
| 6. C3×#424 | C2 | semidirect |
| 7. #3259 | C3 | direct (N × H) |
| 24. #540 | C2×C3 | semidirect |
| 25. #478 | C2×C3 | semidirect |
| 26. #469 | C2×C3 | semidirect |
| 27. #466 | C2×C3 | semidirect |
| 28. #459 | C2×C3 | semidirect |
| 29. #424 | C2×C3 | semidirect |
| 138. C3 | #3259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#540 | 2 |
| C3×#478 | 2 |
| C3×#469 | 2 |
| C3×#466 | 2 |
| C3×#459 | 2 |
| C3×#424 | 2 |
| #3259 | 3 |