Finite Group DatabasebetaFinite Group Databasebeta← Q8×(C3⋊(C3⋊C8))⋊C3 #13142788
Order 1728.
427 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 427 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 4. Q8×C3⋊(C3⋊C8) | C3 | semidirect |
| 18. Q8×H(3,𝔽3) | C8 | semidirect |
| 23. (C3⋊(C3⋊C8))⋊C3 | Q8 | direct (N × H) |
| 56. C32×Q8 | C3⋊C8 | semidirect |
| 57. C32×Q8 | C3×C8 | semidirect |
| 68. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 111. H(3,𝔽3) | C8×Q8 | semidirect |
| 169. C32 | Q8×C3⋊C8 | semidirect |
| 170. C32 | C3×C8×Q8 | semidirect |
| 171. Q8 | (C3⋊(C3⋊C8))⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×H(3,𝔽3) | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| Q8×C3⋊(C3⋊C8) | 3 |
| C3×Q8×C3⋊C8 | 3 |