Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
834 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D33 |
| commutator, cosocle | C2×C33 | C24 |
| Frattini | C2 | C2×D33 |
| Fitting, socle | C22×C33 | C23 |
| hypocenter | C33 | C2×#41 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6296 | C2 | semidirect |
| 2. C2×D3×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C3×#625 | C2 | semidirect |
| 4. #88963 | C2 | direct (N × H) |
| 9. #6296 | C22 | semidirect |
| 10. D3×C3⋊Dic3 | C22 | semidirect |
| 11. C3×#625 | C22 | semidirect |
| 15. C2×#625 | D3 | semidirect |
| 37. #625 | C2×D3 | semidirect |
| 40. C2×C33 | #41 | semidirect |
| 66. C33 | C2×#41 | semidirect |
| 87. C2×C32 | #237 | semidirect |
| 112. C32 | C2×#237 | semidirect |
| 125. C2×C3 | #3805 | semidirect |
| 135. C3 | C2×#3805 | semidirect |
| 137. C2 | #88963 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6296 | 2 |
| C2×D3×C3⋊Dic3 | 2 |
| C2×C3×#625 | 2 |
| #88963 | 2 |
| C2×#3805 | 3 |