Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
636 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22623080 | C2 | semidirect |
| 2. #22621735 | C2 | semidirect |
| 3. #22612053 | C2 | semidirect |
| 4. #22612009 | C2 | semidirect |
| 5. #22611908 | C2 | semidirect |
| 6. #22611813 | C2 | semidirect |
| 7. #22611769 | C2 | semidirect |
| 8. C73×#2247 | C2 | semidirect |
| 141. #2247 | D73 | semidirect |
| 147. C73 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623080 | 2 |
| #22621735 | 2 |
| #22612053 | 2 |
| #22612009 | 2 |
| #22611908 | 2 |
| #22611813 | 2 |
| #22611769 | 2 |
| C73×#2247 | 2 |
| #33860 | 73 |