Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22611981 | C2 | semidirect |
| 4. #22608001 | C2 | semidirect |
| 5. #22607979 | C2 | semidirect |
| 7. C8×Q16×C73 | C2 | semidirect |
| 116. C8×Q16 | D73 | semidirect |
| 120. C73 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611981 | 2 |
| #22611971 | 2 |
| #22609537 | 2 |
| #22608001 | 2 |
| #22607979 | 2 |
| #22607976 | 2 |
| C8×Q16×C73 | 2 |
| #12429 | 73 |