Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #22611703 | C2 | semidirect |
| 5. #22610722 | C2 | semidirect |
| 6. #22608016 | C2 | semidirect |
| 7. C73×#1389 | C2 | semidirect |
| 19. #17988399 | C4 | semidirect |
| 38. #14556531 | C2×C4 | semidirect |
| 53. #108×C73 | C2×C4 | semidirect |
| 143. #1389 | D73 | semidirect |
| 145. C73 | #12953 | semidirect |
| 188. #108 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618782 | 2 |
| #22611703 | 2 |
| C2×#17988401 | 2 |
| C2×#17988399 | 2 |
| #22610722 | 2 |
| #22608016 | 2 |
| C73×#1389 | 2 |
| #12953 | 73 |