Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 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 | C2×C4 | C23×D3 |
| commutator, socle | C22×C3 | C23×C4 |
| Fitting | C3×#424 | C2 |
| prime radical | C23×C3 | C22×C4 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #424 | D3 |
| hypocenter | C3 | #2961 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #4831 | C2 | semidirect |
| 9. #4828 | C2 | semidirect |
| 60. C2×C3⋊C8 | Q8 | semidirect |
| 163. C3 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| C3×#424 | 2 |
| #5122 | 2 |
| #5118 | 2 |
| #5102 | 2 |
| C2×#815 | 2 |
| #4997 | 2 |
| #4831 | 2 |
| #4828 | 2 |
| #2961 | 3 |