Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
362 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 3. Q8⋊#11924031 | C2 | semidirect |
| 78. Q8×C73 | M32 | semidirect |
| 121. C73 | #11607 | semidirect |
| 195. Q8 | #14556665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C4×#14556665 | 2 |
| Q8⋊#11924031 | 2 |
| C2×Q8×#10596831 | 2 |
| #11607 | 73 |