Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22621541 | C2 | semidirect |
| 2. #22612195 | C2 | semidirect |
| 3. #22609407 | C2 | semidirect |
| 4. #22607975 | C2 | semidirect |
| 5. #22607898 | C2 | semidirect |
| 6. #22607888 | C2 | semidirect |
| 7. C73×#2206 | C2 | semidirect |
| 19. #17988363 | C22 | semidirect |
| 20. #17988338 | C22 | semidirect |
| 23. #493×C73 | C22 | semidirect |
| 25. C4⋊C16×C73 | C22 | semidirect |
| 107. D8×C73 | D8 | semidirect |
| 182. #2206 | D73 | semidirect |
| 187. C73 | #12324 | semidirect |
| 194. #493 | C2×D73 | semidirect |
| 202. C4⋊C16 | C2×D73 | semidirect |
| 275. D8 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621541 | 2 |
| #22612195 | 2 |
| #22609407 | 2 |
| #22607975 | 2 |
| #22607898 | 2 |
| #22607888 | 2 |
| C73×#2206 | 2 |
| #12324 | 73 |