Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 229 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×#533 | C2 |
| prime radical | C23×C3 | C22×C4 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #533 | D3 |
| hypocenter | C3 | #2960 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #533 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5024 | C2 | semidirect |
| 3. Q8×C3⋊C8 | C2 | semidirect |
| 44. C2×C3⋊C8 | Q8 | semidirect |
| 131. C3 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #5024 | 2 |
| Q8×C3⋊C8 | 2 |
| #4999 | 2 |
| #4997 | 2 |
| #4924 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #2960 | 3 |