Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×C3×#135 | C2 | semidirect |
| 2. C2×#828 | C2 | semidirect |
| 3. C2×#826 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4562 | C2 | semidirect |
| 7. #4549 | C2 | semidirect |
| 24. C2×#135 | D3 | semidirect |
| 41. C3×Q16 | D4 | semidirect |
| 44. C3×D8 | D4 | semidirect |
| 101. Q16 | #67 | semidirect |
| 106. D8 | #67 | semidirect |
| 172. C3 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| C2×#828 | 2 |
| C2×#826 | 2 |
| #5115 | 2 |
| #4564 | 2 |
| #4562 | 2 |
| #4549 | 2 |
| #2186 | 3 |