Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×#413 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5139 | C2 | semidirect |
| 5. #5131 | C2 | semidirect |
| 13. C2×#235 | C4 | semidirect |
| 15. C22×D12 | C4 | semidirect |
| 17. C2×C3×M16 | C22 | semidirect |
| 18. #926 | C22 | semidirect |
| 27. #413 | D3 | semidirect |
| 74. C2×M16 | C2×D3 | semidirect |
| 222. C3 | #1795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C3×#413 | 2 |
| #5240 | 2 |
| #5139 | 2 |
| #5131 | 2 |
| #1795 | 3 |