Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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, cosocle | C23×C3 | C24 |
| Fitting | C3×#389 | C2 |
| prime radical | C22×D12 | C22 |
| hypercenter | #389 | D3 |
| hypocenter | C3 | #2683 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#897 | C2 | semidirect |
| 2. C2×#896 | C2 | semidirect |
| 3. C3×#389 | C2 | semidirect |
| 4. #4994 | C2 | semidirect |
| 5. #4994 | C2 | semidirect |
| 7. #4928 | C2 | semidirect |
| 9. #4656 | C2 | semidirect |
| 41. #389 | D3 | semidirect |
| 54. C2×D12 | Q8 | semidirect |
| 63. C3×C4⋊C4 | D4 | semidirect |
| 73. C4⋊Dic3 | D4 | semidirect |
| 160. C4⋊C4 | D12 | semidirect |
| 254. C3 | #2683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#897 | 2 |
| C2×#896 | 2 |
| C3×#389 | 2 |
| #4994 | 2 |
| #4939 | 2 |
| #4928 | 2 |
| #4665 | 2 |
| #4656 | 2 |
| #2683 | 3 |