Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1060 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22620679 | C2 | semidirect |
| 2. C2×#17988721 | C2 | semidirect |
| 3. #22610767 | C2 | semidirect |
| 4. #22609862 | C2 | semidirect |
| 5. #22608499 | C2 | semidirect |
| 6. #22607779 | C2 | semidirect |
| 7. C73×#2433 | C2 | semidirect |
| 31. C22×D292 | D4 | semidirect |
| 37. C22×#10596831 | D4 | semidirect |
| 43. C2×C4⋊Dic73 | D4 | semidirect |
| 55. C22⋊#10596831 | D4 | semidirect |
| 151. C22⋊C4×C73 | D8 | semidirect |
| 271. #2433 | D73 | semidirect |
| 276. C73 | #9946 | semidirect |
| 420. C22⋊C4 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620679 | 2 |
| C2×#17988721 | 2 |
| #22610767 | 2 |
| #22609862 | 2 |
| #22608499 | 2 |
| #22607779 | 2 |
| C73×#2433 | 2 |
| #9946 | 73 |