Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#550 | C2 | semidirect |
| 2. C3×D4×Q8 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. C3×#474 | C2 | semidirect |
| 5. C3×#459 | C2 | semidirect |
| 6. C3×C8×Q8 | C2 | semidirect |
| 7. C3×C4×D8 | C2 | semidirect |
| 8. #3358 | C3 | direct (N × H) |
| 25. #550 | C2×C3 | semidirect |
| 26. D4×Q8 | C2×C3 | semidirect |
| 27. #486 | C2×C3 | semidirect |
| 28. #474 | C2×C3 | semidirect |
| 29. #459 | C2×C3 | semidirect |
| 30. C8×Q8 | C2×C3 | semidirect |
| 31. C4×D8 | C2×C3 | semidirect |
| 71. C3×Q8 | D8 | semidirect |
| 77. C3×D4 | #41 | semidirect |
| 123. Q8 | C3×D8 | semidirect |
| 129. D4 | C3×#41 | semidirect |
| 157. C3 | #3358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#550 | 2 |
| C3×D4×Q8 | 2 |
| C3×#486 | 2 |
| C3×#474 | 2 |
| C3×#459 | 2 |
| C3×C8×Q8 | 2 |
| C3×C4×D8 | 2 |
| #3358 | 3 |