Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
526 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 270 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. #22626345 | C2 | semidirect |
| 2. Q8×#11924031 | C2 | semidirect |
| 40. Q8×D73 | C16 | semidirect |
| 96. C73 | #33496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626345 | 2 |
| Q8×#11924031 | 2 |
| #22626291 | 2 |
| #22626290 | 2 |
| C8×Q8×D73 | 2 |
| #33496 | 73 |