Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 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. #5798 | C2 | semidirect |
| 3. C2×#834 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. #4527 | C2 | semidirect |
| 10. C3×#123 | C4 | semidirect |
| 13. C3×#120 | C4 | semidirect |
| 27. C24×C3 | C2×C4 | semidirect |
| 40. C22×C3×C4 | C2×C4 | semidirect |
| 49. C3×C22⋊C4 | C2×C4 | semidirect |
| 54. #217 | D4 | semidirect |
| 60. #123 | Dic3 | semidirect |
| 63. #120 | Dic3 | semidirect |
| 103. C24 | C2×Dic3 | semidirect |
| 119. C22×C4 | C2×Dic3 | semidirect |
| 131. C22⋊C4 | C2×Dic3 | semidirect |
| 216. C3 | #1913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#534 | 2 |
| #5798 | 2 |
| C2×#834 | 2 |
| #4527 | 2 |
| #1913 | 3 |