Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C3 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#578 | C2 | semidirect |
| 2. C3×#510 | C2 | semidirect |
| 3. C3×#508 | C2 | semidirect |
| 4. C2×C3×Q32 | C2 | semidirect |
| 5. C3×#504 | C2 | semidirect |
| 6. #3417 | C3 | direct (N × H) |
| 18. #578 | C2×C3 | semidirect |
| 19. #510 | C2×C3 | semidirect |
| 20. #508 | C2×C3 | semidirect |
| 21. C2×Q32 | C2×C3 | semidirect |
| 22. #504 | C2×C3 | semidirect |
| 95. C3 | #3417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#578 | 2 |
| C3×#510 | 2 |
| C3×#508 | 2 |
| C2×C3×Q32 | 2 |
| C3×#504 | 2 |
| #3417 | 3 |