Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22618567 | C2 | semidirect |
| 3. #22608529 | C2 | semidirect |
| 4. #22608263 | C2 | semidirect |
| 5. #22607825 | C2 | semidirect |
| 6. #22607823 | C2 | semidirect |
| 7. C73×#1527 | C2 | semidirect |
| 54. #14556502 | D4 | semidirect |
| 74. #97×C73 | D4 | semidirect |
| 222. #1527 | D73 | semidirect |
| 226. C73 | #9389 | semidirect |
| 287. #97 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618567 | 2 |
| #22615620 | 2 |
| #22608529 | 2 |
| #22608263 | 2 |
| #22607825 | 2 |
| #22607823 | 2 |
| C73×#1527 | 2 |
| #9389 | 73 |