Finite Group DatabasebetaFinite Group Databasebeta← Q8×C3⋊((C22⋊C9)⋊C2) #13164485
Order 1728.
860 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 109 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. C3×Q8×C22⋊C9 | C2 | semidirect |
| 3. #11722377 | C2 | semidirect |
| 17. Q8×C22⋊C9 | D3 | semidirect |
| 21. C3⋊((C22⋊C9)⋊C2) | Q8 | direct (N × H) |
| 46. C3×C22⋊C9 | C2×Q8 | semidirect |
| 49. C22×C3×Q8 | D9 | semidirect |
| 127. C22⋊C9 | D3×Q8 | semidirect |
| 131. C22×Q8 | C3⋊D9 | semidirect |
| 146. C3×Q8 | (C22⋊C9)⋊C2 | semidirect |
| 194. C22×C3 | Q8×D9 | semidirect |
| 220. Q8 | C3⋊((C22⋊C9)⋊C2) | direct (N × H) |
| 243. C22 | Q8×C3⋊D9 | semidirect |
| 249. C3 | Q8×(C22⋊C9)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×C22⋊C9 | 2 |
| C4×C3⋊((C22⋊C9)⋊C2) | 2 |
| #11722377 | 2 |
| Q8×#638 | 3 |
| Q8×(C22⋊C9)⋊C2 | 3 |
| Q8×C3⋊D9 | 4 |