Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
588 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 132 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 | #379 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C2×C3×H(5,𝔽2) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#421 | C2 | semidirect |
| 3. C3×#418 | C2 | semidirect |
| 4. C3×#413 | C2 | semidirect |
| 5. C3×#410 | C2 | semidirect |
| 6. #1795 | C3 | direct (N × H) |
| 10. C2×C3×#41 | C4 | semidirect |
| 15. C22×C3×D4 | C4 | semidirect |
| 17. C2×C3×M16 | C22 | semidirect |
| 18. C3×#117 | C22 | semidirect |
| 25. #421 | C2×C3 | semidirect |
| 26. #418 | C2×C3 | semidirect |
| 27. #413 | C2×C3 | semidirect |
| 28. #410 | C2×C3 | semidirect |
| 67. C2×#41 | C3×C4 | semidirect |
| 72. C22×D4 | C3×C4 | semidirect |
| 74. C2×M16 | C22×C3 | semidirect |
| 75. #117 | C22×C3 | semidirect |
| 222. C3 | #1795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| C3×#421 | 2 |
| C3×#418 | 2 |
| C3×#413 | 2 |
| C3×#410 | 2 |
| #1795 | 3 |