Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
970 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 970 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 28. #14556652 | Q8 | direct (N × H) |
| 96. Q8×C73 | #101 | semidirect |
| 146. C73 | Q8×#101 | semidirect |
| 240. Q8 | #14556652 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924037 | 2 |
| #22626124 | 2 |
| #22625797 | 2 |
| C4×#14556652 | 2 |
| C2×Q8×Dic146 | 2 |
| Q8×#101 | 73 |