Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1030 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 267 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. C2×#17988985 | C2 | semidirect |
| 3. C2×#17988960 | C2 | semidirect |
| 4. C2×#17988934 | C2 | semidirect |
| 5. #22609559 | C2 | direct (N × H) |
| 6. C2×#322×C73 | C2 | semidirect |
| 13. #17988985 | C22 | semidirect |
| 17. #17988960 | C22 | semidirect |
| 19. #17988934 | C22 | semidirect |
| 24. #322×C73 | C22 | semidirect |
| 82. C2×C8×C73 | SD16 | semidirect |
| 114. C8×C73 | C2×SD16 | semidirect |
| 130. C2×C73 | #1715 | semidirect |
| 140. C2×#322 | D73 | semidirect |
| 141. C73 | C2×#1715 | semidirect |
| 159. #322 | C2×D73 | semidirect |
| 213. C2×C8 | #11924017 | semidirect |
| 249. C8 | C2×#11924017 | semidirect |
| 266. C2 | #22609559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988985 | 2 |
| C2×#17988964 | 2 |
| C2×#17988960 | 2 |
| C2×#17988934 | 2 |
| #22609559 | 2 |
| C2×#322×C73 | 2 |
| C2×#1715 | 73 |