Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#830 | C2 | semidirect |
| 3. #4528 | C2 | semidirect |
| 4. #4525 | C2 | semidirect |
| 26. C2×C3×D4 | C8 | semidirect |
| 65. C23×C3 | C2×C8 | semidirect |
| 83. C2×C3×C4 | C2×C8 | semidirect |
| 90. C2×D4 | C3⋊C8 | semidirect |
| 137. C23 | C2×C3⋊C8 | semidirect |
| 154. C2×C4 | C2×C3⋊C8 | semidirect |
| 187. C3 | #1459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C2×#830 | 2 |
| #4528 | 2 |
| #4525 | 2 |
| #1459 | 3 |