Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 113. Q8×C73 | #108 | semidirect |
| 176. C73 | #8907 | semidirect |
| 285. Q8 | #14556662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924038 | 2 |
| #22626045 | 2 |
| #22625489 | 2 |
| #22625260 | 2 |
| #22624823 | 2 |
| #22624763 | 2 |
| Q8⋊C8×D73 | 2 |
| #8907 | 73 |