Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #4960 |
| commutator, cosocle | C22×C3×C4 | C23 |
| Frattini | C22×C4 | C22×D3 |
| Fitting | C3×#410 | C2 |
| socle | C2×C3 | #392 |
| hypercenter | #410 | D3 |
| hypocenter | C3 | #2008 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #410 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5822 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. #5525 | C2 | semidirect |
| 4. C3×#410 | C2 | semidirect |
| 5. #5005 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 37. #410 | D3 | semidirect |
| 44. C2×C3×Q8 | D4 | semidirect |
| 46. C2×C3×D4 | D4 | semidirect |
| 80. #208 | D4 | semidirect |
| 82. C2×C3⋊C8 | D4 | semidirect |
| 156. C2×Q8 | D12 | semidirect |
| 167. C2×D4 | D12 | semidirect |
| 277. C3 | #2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5822 | 2 |
| C2×#949 | 2 |
| #5525 | 2 |
| C3×#410 | 2 |
| #5005 | 2 |
| #5001 | 2 |
| #4533 | 2 |
| #2008 | 3 |