Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C2×D4 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C24×C3 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C23×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#107 | C2 | semidirect |
| 4. C3×#340 | C2 | semidirect |
| 5. #1808 | C3 | direct (N × H) |
| 8. C22×C3×C8 | C4 | semidirect |
| 16. C2×#107 | C2×C3 | semidirect |
| 18. #340 | C2×C3 | semidirect |
| 37. C22×C8 | C3×C4 | semidirect |
| 63. C3×C8 | C22⋊C4 | semidirect |
| 84. C22×C3 | #107 | semidirect |
| 114. C8 | C3×C22⋊C4 | semidirect |
| 125. C22 | C3×#107 | semidirect |
| 136. C3 | #1808 | 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×#107 | 2 |
| C3×#380 | 2 |
| C3×#340 | 2 |
| #1808 | 3 |