Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C22×C3 | C23×C4 |
| Fitting | C2×C3×#125 | C2 |
| socle, prime radical, cosocle | C23×C3 | C24 |
| hypercenter | C2×#125 | D3 |
| hypocenter | C3 | C4×#125 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C3×#125 | C4 | semidirect |
| 47. #125 | Dic3 | direct (N × H) |
| 109. Dic3 | #125 | direct (N × H) |
| 147. C3 | C4×#125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#125 | 2 |
| #4984 | 2 |
| #4980 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4936 | 2 |
| C42×Dic3 | 2 |
| C4×#125 | 3 |