Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
640 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22618955 | C2 | semidirect |
| 3. #22608498 | C2 | semidirect |
| 4. #22607809 | C2 | semidirect |
| 5. C73×#1799 | C2 | semidirect |
| 12. #17988517 | C4 | semidirect |
| 13. #17988512 | C4 | semidirect |
| 14. #17988504 | C4 | semidirect |
| 15. #17988496 | C4 | semidirect |
| 45. C22⋊#10596831 | D4 | semidirect |
| 221. #1799 | D73 | semidirect |
| 224. C73 | #9384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618955 | 2 |
| #22614887 | 2 |
| #22608498 | 2 |
| #22607809 | 2 |
| C73×#1799 | 2 |
| #9384 | 73 |