Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×#6180 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 4. #88430 | C2 | direct (N × H) |
| 12. #6180 | C22 | semidirect |
| 13. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 43. C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 48. C2×H(3,𝔽3) | M16 | semidirect |
| 80. H(3,𝔽3) | C2×M16 | semidirect |
| 106. C2×C32 | ΓL(1,𝔽25) | semidirect |
| 107. C2×C32 | #208 | semidirect |
| 138. C32 | C2×ΓL(1,𝔽25) | semidirect |
| 139. C32 | C2×#208 | semidirect |
| 169. C2 | #88430 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×(C3⋊D3)⋊C3 | 2 |
| C2×#6180 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #88430 | 2 |
| C2×#3712 | 3 |
| C2×#3711 | 3 |