Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
764 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 293 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, prime radical | C22×C3×#41 | C2 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | C22×#41 | D3 |
| hypocenter | C3 | #2879 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#208 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5207 | C2 | semidirect |
| 16. C2×#208 | C22 | semidirect |
| 17. C22×C3⋊C8 | C22 | semidirect |
| 18. #830 | C22 | semidirect |
| 161. C3 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C22×#208 | 2 |
| #5234 | 2 |
| #5207 | 2 |
| #2879 | 3 |