Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#816 | C2 | semidirect |
| 5. #4551 | C2 | semidirect |
| 17. #924 | C4 | semidirect |
| 120. C22×C3 | #103 | semidirect |
| 169. C22 | #816 | semidirect |
| 182. C3 | #1892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C8 | 2 |
| C2×#924 | 2 |
| #5212 | 2 |
| C2×#816 | 2 |
| #4551 | 2 |
| #1892 | 3 |