Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 108 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. #22625658 | C2 | semidirect |
| 2. C2×#17989438 | C2 | semidirect |
| 3. #22625107 | C2 | semidirect |
| 18. #17988490 | C4 | semidirect |
| 19. #17988457 | C4 | semidirect |
| 20. C2×#127×C73 | C4 | semidirect |
| 24. #14556648 | D4 | semidirect |
| 205. C73 | #9684 | semidirect |
| 206. C2×#127 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625658 | 2 |
| C2×#17989438 | 2 |
| #22625107 | 2 |
| #22618273 | 2 |
| #9684 | 73 |