Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626165 | C2 | semidirect |
| 2. #22625603 | C2 | semidirect |
| 3. #22624902 | C2 | semidirect |
| 4. #22624901 | C2 | semidirect |
| 8. #17989484 | C22 | semidirect |
| 11. #17989455 | C22 | semidirect |
| 12. C2×D8×D73 | C4 | semidirect |
| 16. #17988840 | C4 | semidirect |
| 20. #106×D73 | C4 | semidirect |
| 22. #469×C73 | C4 | semidirect |
| 36. C2×D584 | C2×C4 | semidirect |
| 54. #14556523 | C2×C4 | semidirect |
| 59. C2×D8×C73 | C2×C4 | semidirect |
| 62. #106×C73 | C2×C4 | semidirect |
| 203. D73 | #1339 | semidirect |
| 209. C73 | C2×#1339 | semidirect |
| 220. #469 | #64408 | semidirect |
| 234. C2×D8 | C2×#64408 | semidirect |
| 263. #106 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626165 | 2 |
| #22625603 | 2 |
| #22624902 | 2 |
| #22624901 | 2 |
| #469×D73 | 2 |
| C2×#1339 | 73 |