Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 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×#17988422 | C2 | direct (N × H) |
| 3. C22×#14556497 | C2 | semidirect |
| 4. C22×D16×C73 | C2 | semidirect |
| 7. C2×D1168 | C22 | semidirect |
| 8. #17988422 | C22 | direct (N × H) |
| 9. C2×#14556497 | C22 | semidirect |
| 12. C2×D16×C73 | C22 | semidirect |
| 18. D1168 | C23 | semidirect |
| 19. #14556497 | C23 | semidirect |
| 25. D16×C73 | C23 | semidirect |
| 58. C22×C73 | D32 | semidirect |
| 66. C2×C73 | C2×D32 | semidirect |
| 70. C22×D16 | D73 | semidirect |
| 73. C73 | C22×D32 | semidirect |
| 79. C2×D16 | C2×D73 | semidirect |
| 93. D16 | C22×D73 | semidirect |
| 129. C22 | #17988422 | direct (N × H) |
| 135. C2 | C2×#17988422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1168 | 2 |
| C2×#17988422 | 2 |
| C22×#14556497 | 2 |
| C22×D16×C73 | 2 |
| C22×D32 | 73 |