Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4 | C23 |
| commutator | C22 | C2×C3×C42 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| socle | C23×C3 | C22×C4 |
| prime radical | C24×C3 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3×#97 | C2 | semidirect |
| 5. C3×#336 | C2 | semidirect |
| 6. #1752 | C3 | direct (N × H) |
| 9. C22×C3×C8 | C4 | semidirect |
| 15. C3×C22⋊C8 | C4 | semidirect |
| 20. C2×#97 | C2×C3 | semidirect |
| 22. #336 | C2×C3 | semidirect |
| 44. C22×C8 | C3×C4 | semidirect |
| 50. C22⋊C8 | C3×C4 | semidirect |
| 72. C3×C8 | C22⋊C4 | semidirect |
| 95. C22×C3 | #97 | semidirect |
| 124. C8 | C3×C22⋊C4 | semidirect |
| 133. C22 | C3×#97 | semidirect |
| 143. C3 | #1752 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C8 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×C3×#97 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C3×#336 | 2 |
| #1752 | 3 |