Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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. C22×C3×C4⋊C4 | C2 | semidirect |
| 3. C23×C3⋊C8 | C2 | semidirect |
| 4. C2×#809 | C2 | direct (N × H) |
| 11. C22×D12 | C4 | semidirect |
| 14. C2×C3×C4⋊C4 | C22 | semidirect |
| 16. C22×C3⋊C8 | C22 | semidirect |
| 17. #809 | C22 | direct (N × H) |
| 20. C22×C4⋊C4 | D3 | semidirect |
| 36. C2×D12 | C2×C4 | semidirect |
| 39. C3×C4⋊C4 | C23 | semidirect |
| 41. C2×C3⋊C8 | C23 | semidirect |
| 52. C2×C4⋊C4 | C2×D3 | semidirect |
| 72. D12 | C22×C4 | semidirect |
| 93. C4⋊C4 | C22×D3 | semidirect |
| 94. C22×C3 | #102 | semidirect |
| 127. C2×C3 | C2×#102 | semidirect |
| 136. C22 | #809 | direct (N × H) |
| 145. C3 | C22×#102 | semidirect |
| 147. C2 | C2×#809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#809 | 2 |
| C22×#102 | 3 |