Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D1168 | C2 | semidirect |
| 2. C2×#17989003 | C2 | semidirect |
| 3. #22619580 | C2 | semidirect |
| 4. #22612035 | C2 | semidirect |
| 5. #22612018 | C2 | semidirect |
| 6. #22611646 | C2 | semidirect |
| 7. C73×#2158 | C2 | semidirect |
| 16. C2×#14556530 | C22 | semidirect |
| 17. C2×C16×D73 | C22 | semidirect |
| 19. #17988824 | C22 | semidirect |
| 21. #17988387 | C22 | semidirect |
| 24. #367×C73 | C22 | semidirect |
| 25. #366×C73 | C22 | semidirect |
| 50. C2×C16×C73 | D4 | semidirect |
| 135. #2158 | D73 | semidirect |
| 137. C73 | #33607 | semidirect |
| 153. #367 | C2×D73 | semidirect |
| 154. #366 | C2×D73 | semidirect |
| 179. C2×C16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1168 | 2 |
| C2×#17989003 | 2 |
| #22619580 | 2 |
| #22612035 | 2 |
| #22612018 | 2 |
| #22611646 | 2 |
| C73×#2158 | 2 |
| #33607 | 73 |