Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
524 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C2×C3×#95 | C2 |
| prime radical | C24×C3 | C23 |
| hypercenter | C2×#95 | D3 |
| hypocenter | C3 | #2659 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4661 | C2 | semidirect |
| 5. #4656 | C2 | semidirect |
| 28. C22×C3×C4 | Q8 | semidirect |
| 78. C22×C4 | Dic6 | semidirect |
| 140. C3 | #2659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#924 | 2 |
| C2×C3×#95 | 2 |
| #5212 | 2 |
| #4661 | 2 |
| #4656 | 2 |
| #2659 | 3 |