Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22612187 | C2 | semidirect |
| 3. #22612160 | C2 | semidirect |
| 4. #22609536 | C2 | semidirect |
| 5. #22609524 | C2 | semidirect |
| 6. #22607850 | C2 | semidirect |
| 7. C73×#2240 | C2 | semidirect |
| 116. #2240 | D73 | semidirect |
| 120. C73 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612187 | 2 |
| #22612180 | 2 |
| #22612160 | 2 |
| #22609536 | 2 |
| #22609524 | 2 |
| #22607850 | 2 |
| C73×#2240 | 2 |
| #12527 | 73 |