Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22622940 | C2 | semidirect |
| 2. #22612196 | C2 | semidirect |
| 3. #22611995 | C2 | semidirect |
| 4. #22611983 | C2 | semidirect |
| 5. #22611964 | C2 | semidirect |
| 6. #22611839 | C2 | semidirect |
| 7. #22611796 | C2 | semidirect |
| 8. C4×D1168 | C2 | semidirect |
| 9. C73×#2249 | C2 | semidirect |
| 152. #2249 | D73 | semidirect |
| 159. C73 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622940 | 2 |
| #22612196 | 2 |
| #22611995 | 2 |
| #22611983 | 2 |
| #22611964 | 2 |
| #22611839 | 2 |
| #22611796 | 2 |
| C4×D1168 | 2 |
| C73×#2249 | 2 |
| #33970 | 73 |