Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
639 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. Q8×C9×A4 | C2 | semidirect |
| 3. A4×Dic18 | C2 | semidirect |
| 5. C22×Q8×D9 | C3 | semidirect |
| 13. C22×Q8×C9 | C2×C3 | semidirect |
| 19. C22×Dic18 | C2×C3 | semidirect |
| 22. A4×D9 | Q8 | direct (N × H) |
| 43. Q8×D9 | A4 | direct (N × H) |
| 53. C9×A4 | C2×Q8 | semidirect |
| 65. Q8×A4 | D9 | direct (N × H) |
| 76. C22×D9 | C3×Q8 | semidirect |
| 81. Q8×C9 | C2×A4 | semidirect |
| 94. Dic18 | C2×A4 | semidirect |
| 128. C22×C9 | C2×C3×Q8 | semidirect |
| 146. C22×Q8 | C3×D9 | semidirect |
| 184. D9 | Q8×A4 | direct (N × H) |
| 215. A4 | Q8×D9 | direct (N × H) |
| 225. C9 | C2×Q8×A4 | semidirect |
| 237. Q8 | A4×D9 | direct (N × H) |
| 263. C22 | C3×Q8×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| C4×A4×D9 | 2 |
| A4×Dic18 | 2 |
| D3×Q8×A4 | 3 |
| C22×Q8×D9 | 3 |
| C3×Q8×D9 | 4 |