Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #5091 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 6. #5031 | C2 | semidirect |
| 7. #5021 | C2 | semidirect |
| 105. C2×C3×C4 | Q16 | semidirect |
| 177. C2×C4 | #216 | semidirect |
| 204. C3 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #5470 | 2 |
| #5091 | 2 |
| #5090 | 2 |
| #5051 | 2 |
| #5031 | 2 |
| #5021 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #3249 | 3 |