Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C3⋊C8 | C2 | semidirect |
| 3. D4×C3⋊C8 | C2 | semidirect |
| 4. #4925 | C2 | semidirect |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 25. C3×#41 | C8 | semidirect |
| 55. C3×Q8 | C2×C8 | semidirect |
| 56. C3×D4 | C2×C8 | semidirect |
| 59. C2×C3×C4 | C2×C8 | semidirect |
| 67. C3⋊C8 | #41 | direct (N × H) |
| 68. #41 | C3⋊C8 | direct (N × H) |
| 95. Q8 | C2×C3⋊C8 | semidirect |
| 96. D4 | C2×C3⋊C8 | semidirect |
| 99. C2×C4 | C2×C3⋊C8 | semidirect |
| 122. C3 | C8×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| Q8×C3⋊C8 | 2 |
| D4×C3⋊C8 | 2 |
| #4925 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C8×#41 | 3 |