Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. C3×#336 | C2 | semidirect |
| 4. #4550 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 16. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 22. #336 | D3 | semidirect |
| 37. C2×C3×C8 | C2×C4 | semidirect |
| 43. C2×C3⋊C8 | C2×C4 | semidirect |
| 64. C2×C3×C4 | M16 | semidirect |
| 74. C2×Dic3 | M16 | semidirect |
| 98. C2×C8 | C4×D3 | semidirect |
| 134. C2×C4 | ΓL(1,𝔽25) | semidirect |
| 162. C3 | #1728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| C2×C42×D3 | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| #1728 | 3 |