Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
476 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 344 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 | C4 | C23×C3×C4 |
| Frattini, cosocle | C2×C4 | C24×C3 |
| prime radical | C2×C3×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C2×C3×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#428 | C2 | semidirect |
| 4. C3×#427 | C2 | semidirect |
| 5. C2×C3×#107 | C2 | semidirect |
| 6. #2913 | C3 | direct (N × H) |
| 8. C3×#131 | C4 | semidirect |
| 21. #428 | C2×C3 | semidirect |
| 22. #427 | C2×C3 | semidirect |
| 23. C2×#107 | C2×C3 | semidirect |
| 30. C3×M16 | C2×C4 | semidirect |
| 31. C2×C3×C8 | C2×C4 | semidirect |
| 40. #131 | C3×C4 | semidirect |
| 69. M16 | C2×C3×C4 | semidirect |
| 70. C2×C8 | C2×C3×C4 | semidirect |
| 112. C3 | #2913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C3×#520 | 2 |
| C3×#428 | 2 |
| C3×#427 | 2 |
| C2×C3×#107 | 2 |
| #2913 | 3 |