Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#17988422 | C2 | semidirect |
| 2. #22612017 | C2 | semidirect |
| 3. #22608109 | C2 | semidirect |
| 4. C22⋊#14556497 | C2 | semidirect |
| 5. C22×D16×C73 | C2 | semidirect |
| 6. C2×D1168 | C22 | semidirect |
| 9. C2×#14556497 | C22 | semidirect |
| 10. #17988413 | C22 | semidirect |
| 31. D16×C73 | D4 | semidirect |
| 82. C22×C73 | D32 | semidirect |
| 98. C22×D16 | D73 | semidirect |
| 103. C73 | #13661 | semidirect |
| 126. D16 | C22⋊D73 | semidirect |
| 183. C22 | #17988422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988422 | 2 |
| #22612017 | 2 |
| #22608109 | 2 |
| C22⋊#14556497 | 2 |
| C22×D16×C73 | 2 |
| #13661 | 73 |