Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22619931 | C2 | semidirect |
| 2. #22619397 | C2 | semidirect |
| 3. #22614832 | C2 | semidirect |
| 4. #22608492 | C2 | semidirect |
| 5. #22608321 | C2 | semidirect |
| 6. #22607791 | C2 | semidirect |
| 7. C73×#1486 | C2 | semidirect |
| 42. #14556591 | D4 | semidirect |
| 43. #14556588 | D4 | semidirect |
| 67. C4×#10596831 | D4 | semidirect |
| 83. C4⋊C8×C73 | D4 | semidirect |
| 100. C2×D292 | D8 | semidirect |
| 261. #1486 | D73 | semidirect |
| 264. C73 | #9996 | semidirect |
| 331. C4⋊C8 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619931 | 2 |
| #22619397 | 2 |
| #22614832 | 2 |
| #22608492 | 2 |
| #22608321 | 2 |
| #22607791 | 2 |
| C73×#1486 | 2 |
| #9996 | 73 |