Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #5223 |
| commutator, cosocle | C22×C3×C4 | C23 |
| Frattini | C22×C4 | C22×D3 |
| Fitting | C3×#535 | C2 |
| socle | C2×C3 | #392 |
| hypercenter | #535 | D3 |
| hypocenter | C3 | #2008 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#535 | C2 | semidirect |
| 2. #5822 | C2 | semidirect |
| 3. C2×#932 | C2 | semidirect |
| 4. #5236 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5006 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 34. #535 | D3 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 63. C2×Dic6 | D4 | semidirect |
| 80. #208 | D4 | semidirect |
| 82. C2×C3⋊C8 | D4 | semidirect |
| 277. C3 | #2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5822 | 2 |
| C2×#932 | 2 |
| #5236 | 2 |
| #5215 | 2 |
| #5006 | 2 |
| #4533 | 2 |
| #2008 | 3 |