Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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×#938 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C2×#895 | C2 | semidirect |
| 4. C2×C3×#102 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 34. C2×#102 | D3 | semidirect |
| 45. C2×C3×D4 | D4 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 72. C3×C4⋊C4 | D4 | semidirect |
| 77. C4⋊Dic3 | D4 | semidirect |
| 80. C2×C3⋊C8 | D4 | semidirect |
| 123. C22×D3 | D8 | semidirect |
| 175. C2×D4 | D12 | semidirect |
| 196. C4⋊C4 | #67 | semidirect |
| 332. C3 | #1999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#938 | 2 |
| C22×#213 | 2 |
| C2×#895 | 2 |
| C2×C3×#102 | 2 |
| C2×#821 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4529 | 2 |
| #1999 | 3 |