Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
530 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 241 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. #22627157 | C2 | semidirect |
| 2. Q8×#11924040 | C2 | semidirect |
| 20. #14556687 | Q8 | direct (N × H) |
| 40. #11924040 | C2×Q8 | semidirect |
| 63. Q8×C73 | M32 | semidirect |
| 100. C73 | Q8×M32 | semidirect |
| 158. Q8 | #14556687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627157 | 2 |
| Q8×#11924040 | 2 |
| #22627119 | 2 |
| C4×#14556687 | 2 |
| C2×Q8×#10596833 | 2 |
| Q8×M32 | 73 |