Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #953 |
| commutator, cosocle | C3×C42 | C23 |
| Frattini | C42 | C22×D3 |
| Fitting, prime radical | C3×D42 | C2 |
| socle | C22×C3 | #120 |
| hypercenter | D42 | D3 |
| hypocenter | C3 | #1639 |
| LCS | G ▷ C3×C42 ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5070 | C2 | semidirect |
| 3. #5019 | C2 | semidirect |
| 4. #5007 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. D4⋊(C3⋊C8) | C2 | semidirect |
| 7. D4⋊(C3⋊C8) | C2 | semidirect |
| 18. #869 | C22 | semidirect |
| 23. C4⋊(C3⋊C8) | C22 | semidirect |
| 24. C4⋊(C3⋊C8) | C22 | semidirect |
| 25. C4×C3⋊C8 | C22 | semidirect |
| 93. C3×D4 | SD16 | semidirect |
| 173. D4 | #214 | semidirect |
| 212. C3 | #1639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D42 | 2 |
| #5070 | 2 |
| #5019 | 2 |
| #5007 | 2 |
| #4544 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #1639 | 3 |