Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
468 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 165 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, prime radical, cosocle | C23×C3 | C24 |
| Fitting | C3×#391 | C2 |
| hypercenter | #391 | D3 |
| hypocenter | C3 | #2568 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 41. C2×C3×Q8 | Q8 | semidirect |
| 111. C2×Q8 | Dic6 | semidirect |
| 189. C3 | #2568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| C2×#888 | 2 |
| C3×#391 | 2 |
| #5229 | 2 |
| #4977 | 2 |
| #4936 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4660 | 2 |
| #4646 | 2 |
| #2568 | 3 |