Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626159 | C2 | semidirect |
| 2. #22624854 | C2 | semidirect |
| 3. #22624853 | C2 | semidirect |
| 7. C22⋊#11924031 | C22 | semidirect |
| 175. C73 | #11421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| #22624854 | 2 |
| #22624853 | 2 |
| #408×D73 | 2 |
| #11421 | 73 |