Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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. #22618184 | C2 | direct (N × H) |
| 2. C2×#17988499 | C2 | semidirect |
| 5. C23×Dic146 | C22 | semidirect |
| 7. #17988499 | C22 | semidirect |
| 9. C2×#14556498 | C22 | semidirect |
| 14. C22×Dic146 | C23 | semidirect |
| 18. #14556498 | C23 | semidirect |
| 20. C25×C73 | Q8 | semidirect |
| 37. C24×C73 | C2×Q8 | semidirect |
| 73. C2×C73 | #2840 | semidirect |
| 80. C73 | C2×#2840 | semidirect |
| 90. C25 | Dic146 | semidirect |
| 108. C24 | C2×Dic146 | semidirect |
| 148. C2 | #22618184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618184 | 2 |
| C2×#17988499 | 2 |
| C2×#17988443 | 2 |
| C2×#379×C73 | 2 |
| C2×#2840 | 73 |