Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
522 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 151 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×C9×Dic6 | C2 | semidirect |
| 3. C2×C3×Dic18 | C2 | semidirect |
| 5. C2×#6189 | C2 | semidirect |
| 6. (C3⋊D9)⋊Q8 | C2 | direct (N × H) |
| 15. C9×Dic6 | C22 | semidirect |
| 16. C3×Dic18 | C22 | semidirect |
| 18. #6189 | C22 | semidirect |
| 31. C2×Dic18 | D3 | semidirect |
| 33. C2×C3⋊D9 | Q8 | semidirect |
| 64. Dic18 | C2×D3 | semidirect |
| 65. C2×C3×C9 | C2×Q8 | semidirect |
| 67. C3⋊D9 | C2×Q8 | semidirect |
| 80. C2×Dic6 | D9 | semidirect |
| 101. C3×C9 | C22×Q8 | semidirect |
| 125. Dic6 | C2×D9 | semidirect |
| 131. C2×C9 | D3×Q8 | semidirect |
| 162. C9 | C2×D3×Q8 | semidirect |
| 175. C2×C3 | Q8×D9 | semidirect |
| 190. C3 | C2×Q8×D9 | semidirect |
| 193. C2 | (C3⋊D9)⋊Q8 | 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⋊D9 | 2 |
| C2×C9×Dic6 | 2 |
| C2×C3×Dic18 | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| C2×#6189 | 2 |
| (C3⋊D9)⋊Q8 | 2 |
| C2×#3797 | 3 |
| C2×Q8×D9 | 3 |