Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#924 | C2 | semidirect |
| 3. C22×#204 | C2 | semidirect |
| 4. C2×C3×C22⋊C8 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 35. C2×C22⋊C8 | D3 | semidirect |
| 64. C2×Dic6 | D4 | semidirect |
| 70. C2×C3×C8 | D4 | semidirect |
| 76. C4⋊Dic3 | D4 | semidirect |
| 106. C23×C3 | SD16 | semidirect |
| 182. C2×C8 | #67 | semidirect |
| 232. C23 | #204 | semidirect |
| 305. C3 | #2000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C2×#924 | 2 |
| C22×#204 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4551 | 2 |
| #2000 | 3 |