Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22608754 | C2 | semidirect |
| 3. #22607897 | C2 | semidirect |
| 4. #22607851 | C2 | semidirect |
| 5. C73×#1368 | C2 | semidirect |
| 19. D1168 | C8 | semidirect |
| 32. D584 | C2×C8 | semidirect |
| 43. C16×C73 | C2×C8 | semidirect |
| 71. #1368 | D73 | semidirect |
| 74. C73 | #12067 | semidirect |
| 112. C16 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611808 | 2 |
| #22608754 | 2 |
| #22607897 | 2 |
| #22607851 | 2 |
| C73×#1368 | 2 |
| #12067 | 73 |