Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1168 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D3 |
| commutator | C23×C3 | C22×C4 |
| Fitting, prime radical | C23×C3×D4 | C2 |
| socle, cosocle | C24×C3 | C23 |
| hypercenter | C23×D4 | D3 |
| hypocenter | C3 | #1438 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#217 | C2 | semidirect |
| 3. C2×C3⋊#95 | C2 | semidirect |
| 8. C22×C3×D4 | C4 | semidirect |
| 34. C22×Dic3 | D4 | semidirect |
| 39. C22×D4 | Dic3 | semidirect |
| 58. C23×C3 | C22⋊C4 | semidirect |
| 67. C2×C3×C4 | C22⋊C4 | semidirect |
| 123. C23 | #217 | semidirect |
| 137. C2×C4 | #217 | semidirect |
| 162. C3 | #1438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×#217 | 2 |
| C2×C3⋊#95 | 2 |
| #1438 | 3 |