Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
243 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C23×A4 |
| commutator, cosocle | C2×Q8 | C23×C3 |
| Fitting | #3504 | C3 |
| prime radical | C2×#41⋊C3 | C22 |
| hypercenter | #125 | A4 |
| hypocenter | Q8 | C2×C3×Q8 |
| LCS | G ▷ C2×Q8 ▷ Q8 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #557⋊C3 | C2 | semidirect |
| 4. #3504 | C3 | semidirect |
| 16. #41⋊C3 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #557⋊C3 | 2 |
| #520⋊C3 | 2 |
| C4×#41⋊C3 | 2 |
| #3504 | 3 |
| C3×#125 | 4 |