Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 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. C3×C4×Q16 | C2 | semidirect |
| 2. C2×#828 | C2 | semidirect |
| 4. #4491 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 19. C4×Q16 | D3 | semidirect |
| 27. C3×Q16 | D4 | semidirect |
| 68. Q16 | D12 | semidirect |
| 86. C3×C4 | SD32 | semidirect |
| 115. C4 | #828 | semidirect |
| 118. C3 | #2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q16 | 2 |
| C2×#828 | 2 |
| #4695 | 2 |
| #4491 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2207 | 3 |