Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 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. #22612156 | C2 | semidirect |
| 2. #22612155 | C2 | semidirect |
| 3. #22612154 | C2 | semidirect |
| 5. #22609540 | C2 | semidirect |
| 6. #22607847 | C2 | semidirect |
| 7. C73×#2240 | C2 | semidirect |
| 112. #2240 | D73 | semidirect |
| 116. C73 | #12513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612156 | 2 |
| #22612155 | 2 |
| #22612154 | 2 |
| #22609545 | 2 |
| #22609540 | 2 |
| #22607847 | 2 |
| C73×#2240 | 2 |
| #12513 | 73 |