Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626159 | C2 | semidirect |
| 2. C2×#17989461 | C2 | semidirect |
| 3. #22624919 | C2 | semidirect |
| 4. #22624918 | C2 | semidirect |
| 12. C2×#14556614 | C4 | semidirect |
| 17. #17988823 | C4 | semidirect |
| 20. #17988624 | C4 | semidirect |
| 22. #467×C73 | C4 | semidirect |
| 34. C2×D584 | C2×C4 | semidirect |
| 49. #14556525 | C2×C4 | semidirect |
| 54. C2×Q16×C73 | C2×C4 | semidirect |
| 57. #107×C73 | C2×C4 | semidirect |
| 187. C73 | #11704 | semidirect |
| 194. #467 | #64408 | semidirect |
| 209. C2×Q16 | C2×#64408 | semidirect |
| 235. #107 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626159 | 2 |
| C2×#17989461 | 2 |
| #22624919 | 2 |
| #22624918 | 2 |
| #22619514 | 2 |
| #11704 | 73 |