Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#216 | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4816 | C2 | direct (N × H) |
| 18. C2×#216 | C22 | semidirect |
| 29. C3×#103 | C22 | semidirect |
| 30. #816 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 39. C2×#103 | D3 | semidirect |
| 94. #103 | C2×D3 | semidirect |
| 204. C2×C3 | #470 | semidirect |
| 225. C3 | C2×#470 | semidirect |
| 227. C2 | #4816 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#946 | 2 |
| C22×#216 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#897 | 2 |
| C2×C3×#103 | 2 |
| C2×#816 | 2 |
| C2×#808 | 2 |
| #4816 | 2 |
| C2×#470 | 3 |