Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
628 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C3 | C22×C42 |
| Fitting | C3×C4×C4⋊C4 | C2 |
| socle, prime radical, cosocle | C23×C3 | C24 |
| hypercenter | C4×C4⋊C4 | D3 |
| hypocenter | C3 | #2276 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #887 | C4 | semidirect |
| 22. C4×Dic6 | C4 | semidirect |
| 96. Dic6 | C42 | semidirect |
| 171. C3 | #2276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#887 | 2 |
| C2×C4×Dic6 | 2 |
| C3×C4×C4⋊C4 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4932 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4649 | 2 |
| #4648 | 2 |
| #2276 | 3 |