Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 1. #22612188 | C2 | semidirect |
| 3. C8×#11924003 | C2 | semidirect |
| 4. C73×#1713 | C2 | semidirect |
| 26. #11924003 | D8 | semidirect |
| 40. C8×C73 | SD32 | semidirect |
| 53. #1713 | D73 | semidirect |
| 56. C73 | #12517 | semidirect |
| 92. C8 | #14556534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612188 | 2 |
| #22609546 | 2 |
| C8×#11924003 | 2 |
| C73×#1713 | 2 |
| #12517 | 73 |