Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #4467 | C2 | semidirect |
| 7. C22×Dic6 | C4 | semidirect |
| 12. C2×C4⋊Dic3 | C4 | semidirect |
| 15. #924 | C4 | semidirect |
| 189. C3 | #1520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#924 | 2 |
| C2×C3×C22⋊C8 | 2 |
| #5212 | 2 |
| #4467 | 2 |
| #1520 | 3 |