Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
| prime radical | C2×C3×#41 | C22 |
| 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. C2×C3×#125 | C2 | semidirect |
| 3. C3×#479 | C2 | semidirect |
| 4. C3×#478 | C2 | semidirect |
| 5. C3×#428 | C2 | semidirect |
| 6. C3×#423 | C2 | semidirect |
| 8. #3080 | C3 | direct (N × H) |
| 28. C2×#125 | C2×C3 | semidirect |
| 30. #479 | C2×C3 | semidirect |
| 31. #478 | C2×C3 | semidirect |
| 32. #428 | C2×C3 | semidirect |
| 33. #423 | C2×C3 | semidirect |
| 176. C3 | #3080 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#125 | 2 |
| C3×C4×#41 | 2 |
| C3×#479 | 2 |
| C3×#478 | 2 |
| C3×#428 | 2 |
| C3×#423 | 2 |
| C3×#417 | 2 |
| #3080 | 3 |